Andrew Elfenbein has it right. ‘Victorianists,’ he says, ‘have not been entirely ignorant of Coleridge's tract, but ...' But?
But it is generally relegated to the tomb of intellectual history, a victim of concise paraphrase. Paraphrases do not get Coleridge wrong, but they kill off his intellectual seriousness, ambition, and emotional longing. They do not convey why so many Victorians cared as much as they did about what Coleridge wrote. [Elfenbein, ‘Samuel Taylor Coleridge, On the Constitution of the Church and State (1829)’, Victorian Review 35:1 (Spring 2009), 19]And care they did! This short book directly inspired and informed the political and social theories of John Stuart Mill, Thomas Arnold, Matthew Arnold, Henry Sidwick, F D Maurice and many others. Gladstone called the book 'masterly', and attempted to govern by its principles.
It really deserves to be better known; and for that reason I’m now going to lay out precisely the kind of paraphrase Elfenbein is deprecating in that opening quotation. I’m doing so because it seems to me a useful first step in getting a hold of Church and State. This book, as Peter Allen says, ‘became his most immediately influential work, has inspired a succession of distinguished social critics and remains essential reading in the history of thought on educated elites’; but he’s also spot-on that ‘as descriptive catalogues go Church and State is brilliantly suggestive and maddeningly elliptical.’ [Peter Allen, ‘S. T. Coleridge's Church and State and the Idea of an Intellectual Establishment’, Journal of the History of Ideas 46:1 (1985), 89-106; 89] So let me quickly step through the argument of this short book. I’m going to refer to the different chapters, even thought STC’s first edition doesn’t divide the work that way—Henry Nelson Coleridge’s 1839 edition, issued five years after Coleridge’s death, replaces the first two subheadings (‘Prefatory Remarks’, ‘Concerning the Right Idea of the Constitution’ and so on) with ‘Chapter 1’, ‘Chapter 2’, and then cuts up the remaining block of text into another 10. And I shall follow him, even though it’s the first edition (available free online in its entirety from Google Books) that I’m working from.
Chapter 1 starts with some remarks on the historical circumstance out of which the book was written: ‘the Bill lately passed for the admission of Roman Catholics into the Legislature’ (which is to say: the Roman Catholic Relief Act of 1829). But the third paragraph gets to the meat of the issue without further to-doing. STC defines what he means by ‘Constitution’ and by ‘National Church’.
the true Idea of a CONSTITUTION, and, likewise, of a NATIONAL CHURCH. And in giving the essential character of the latter, I shall briefly specify its distinction from the Church of Christ, and its contra-distinction from a third form, which is neither national nor Christian, but irreconcileable with, and subversive of, both. The latter is a three-part distinction. There is the actual Church (in this case the Anglican Church), made up of its priests and its congregation, owning certain properties such as church-buildings, and performing religious services on Sundays and at other times, and doing all the things Anglicanism does—from organising fêtes on up. That’s A. Then there’s a kind of spiritual perfection of ‘the Church’, what it means to be a member of the body of Christianity in the eyes of God, under the species of eternity. That’s B. Then, Coleridge insists, there is a third thing meant by ‘Church’, which is somehow strung between the two. Park that idea; we’ll come back to it. For now we need to know what STC means by ‘idea’. Not Platonic form—not ‘generally held belief about’ a thing and not an notion abstracted from specific examples of a thing in the world. Coleridge means something much more teleological.
By an idea, I mean, (in this instance) that conception of a thing, which is not abstracted from any particular state, form, or mode, in which the thing may happen to exist at this or at that time; nor yet generalized from any number or succession of such forms or modes; but which is given by the knowledge of its ultimate aim. STC’s idea of the state, and of the Church, is where these two things should be going. In the next paragraph STC says that many people can conceive of what is meant by Church and State, few possess the idea of either. Most people, he says, do not possess an idea, they ‘are possessed by it’. . I'm not sure about that myself, but OK.
He gives the example of Rousseau’s Social Contract. As a ‘conception’, STC says; or something that literally and historically happened, it is clearly bobbins: ‘at once false and foolish’. No two humans ever signed such a contract, thereby inspiring others to structure society according to the rational equity of contractualism. But, says Coleridge, as an idea, the social contract is a powerful good.
But if instead of the conception or theory of an original social contract, we say the idea of an ever-originating social contract, this is so certain and so indispensable, that it constitutes the whole ground of the difference between subject and serf, between a commonwealth and a slave-plantation. And this, again, is evolved out of the yet higher idea of person in contra-distinction from thing—all social law and justice being grounded on the principle that a person can never, but by his own fault, become a thing, or, without grievous wrong, be treated as such; and the distinction consisting in this, that a thing may be used altogether and merely as the means to an end; but the person must always be included in the end: [7-8]This, of course, is a Kantian ethics; and quite right too. What’s distinctively Coleridgean is the notion that the ‘social contract’ is valuable inasmuch as it tends towards an ideal future in which we contract freely with one another as autonomous individuals, each treating each always as an ends in itself rather than as a means to an end.
So, STC insists, with ‘free will’; it makes more ethical sense to think of this as an ‘idea’ than to delve into the brain chemistry of it as an actual fact. Thus, says Coleridge, the ‘Constitution’ of the State. There is no actual British Constitution; but the idea of the Constitution is demonstrated by ‘our whole history from Alfred onward’ . It is a principle, and thus exists ‘in the only way in which a principle can exist,—in the minds and consciences of the persons whose duties it prescribes, and whose rights it determines. In the same sense that the sciences of arithmetic and of geometry, that mind, that life itself, have reality ; the Constitution has real existence, and does not the less exist in reality, because it both is, and exists as, an IDEA.’ He goes on to compare ‘life’ as determined by ‘a vital principle’; and draws a parallel with the planets orbiting the sun. Kepler and Newton established certain facts about orbital mechanics, which is all to the good; ‘but the principle of gravity, the law in the material creation, the idea of the Creator, is pre-supposed in order to the existence, yea, to the very conception of the existence, of matter itself.’ 
He ends the first chapter by lamenting the potential confusion of the term ‘State’. There are, he says, two senses in which the word signifies: there’s a larger sense, where State means ‘the entire realm, including the Church’ and a narrower sense in which the State is the secular architecture of social life, distinguished from the spiritual and religious architecture we call Church.
Chapter 2 picks up on this, and explores ‘the Idea of a State in the larger sense of the term, introductory to the constitution of the State in the narrower sense’. The main theme here is that the state is a balance—I’m tempted to say, a dialectic—of ‘permanence’ and ‘progression’. He glances at Roman history before setting out his stall: there are two main power blocs in modern society: on the one hand ‘the agricultural or possessors of land’ and on the other the ‘citizens’ (‘the mercantile, the manufacturing, the distributive, and the professional bodies, under the common name of citizens’). The former, broadly, want to keep things as they have always been; the latter, broadly, want to change things—as they see it, to change things for the better. The chapter then gallops through several historical examples: Dante’s Florence was a free principality, but Austria and Spain have degraded Italy into a feudal state, running-down commercial innovation and concentrating all power in the landowners' hands, such that Italy is now a nation of slaves ‘from the Alps to the Straits of Messina’. Britain, STC argues, is better placed: because the landowners own half the means of legislation—that is, the House of Lords—and the citizens own the other half—the House of Commons—with the monarch, by granting or withholding royal assent, acting as a kind of ‘beam’ or halfway point.
That harmonious balance of the two great correspondent, at once supporting and counterpoising, interests of the State, its permanence, and its progression; that balance of the landed and the personal interests was to be secured by a legislature of two Houses; the first consisting wholly of barons or landholders, permanent and hereditary senators; the second of the knights or minor barons, elected by, and as the representatives of, the remaining landed community, together with the burgesses, the representatives of the commercial, manufacturing, distributive, and professional classes, — the latter (the elected burgesses) constituting the major number. The king, meanwhile, in whom the executive power is vested, it will suffice at present to consider as the beam of the constitutional scales. And so to the two brief chapters 3: ‘on the National Church’ [30-35] and 4 ‘the Hebrew Commonwealth’ [35-42]. Here Coleridge sketches a history of religious establishment, drawing on the origins of ‘the church’ amongst the Scandinavian, Celtic, Gothic and Semitic tribes. This strikes me as a slightly eccentric narrative, but fair enough: nations get established, and land is distributed between ‘individual warriors’ and ‘heads of families’ and suchlike aristocrats; but the whole wealth of the land is not snaffled up by these people; a ‘reserve’ (what STC called the ‘Nationality’, opposed to the ‘Propriety’ of individual estates) is set aside ‘for the nation itself’. Chapter 4 then elaborates one specific example of this from the history of Israel. Twelve tribes, eleven of which divided the ‘Propriety’ amongst themselves; but Moses insists each have to pay a tithe to the tribe of Levi, who are intrusted not only with the material ‘Nationality’ of this commonwealth but also, and more importantly, with the duty of advance the ‘moral and intellectual character’ of the nation.
The implication of this chapter is that Coleridge could tell a similar history concerning ‘the Celtic, Gothic, and Scandinavian’, but with two crucial salient differences. One is that these tribes have been historically feudal in essence, and more-or-less hostile to the mercantile and professional classes—where with Solomon the Jewish people actively embraced such (as we would say nowadays) ‘wealth-creating’ opportunities—hence all the Jewish merchants, money-lenders and professionals. The other is that these other tribes were polytheistic where the Jews were monotheistic. Both these things, STC thinks, are relevant to the history of Christianity.
relatively to the Jewish polity, the Jehovah was their covenanted king: and if we draw any inference from the former, the Christian sense of the term, it should be this—that God is the unity of every nation; that the convictions and the will, which are one, the same, and simultaneously acting in a multitude of individual agents, are not the birth of any individual; “that when the people speak loudly and unanimously, it is from their being strongly impressed by the godhead or the demon. Only exclude the (by no means extravagant) supposition of a demoniac possession, and then Vox Populi Vox Dei.” That last bit loosely quoted from William Wordsworth’s Convention of Cintra (1808). Anyhow, Coleridge closes this chapter with the notion that ‘it was in the name of the KING, in whom both the propriety and the nationalty ideally centered.’
The second part of this read-through is here.