I confess I don't think I understand what Fr Tim Finigan and Fr Ray Blake mean when they say the Church should, or could, 'get out of the State marriage business'. Fr Tim mentions Bishop Egan on this, but Bishop Egan is talking about being 'forced out' of involvement in marriage registration, not going voluntarily.
The two blogging priests seem to be concerned that, assuming the current legislation is passed and the definition of marriage in civil law comes to mean simply a souped-up friendship with hospital visiting rights and certain tax advantages, it is not something they want anything to do with. That is understandable, but one of the confusions introduced by the Government was to invent a distinction between 'state marriage' and 'religious marriage', a distinction which does not exist. There is only marriage: natural marriage, and the sacramental marriage which, when the parties are baptised, supervenes upon it. Marriage is an institution of natural law, and it is recognised by both Church and state.
Currently, the State recognises marriage, but regulates it: it specifies impediments, for example age and consanguinity, which may presumably by tighter or looser than those demanded by Natural Law. (The Church, in fact, does the same thing, and so Catholics seeking married must satisfy both set of requirements.) Because the law of the land sets what is socially recognised as marriage, it is impossible to get married in England and Wales without going through a ceremony recognised by the law of the land. No one would regard you are married. No one seeking marriage would seek it in a way incompatible with legal recognition. Marriage is by its nature a public act, being married is a to be in a certain social category. People seeking marriage will ipso facto want the recognition of the law.
The state also allows people to get married who are not, under Natural or Divine Law, free to marry: people who have a validly married spouse still living, for example. We say of such people that they are not 'really' married, and at this point what is recognised socially becomes less clear. But if the law of the land wants to do this, while it confuses and weakens the social recognition of the institution, it doesn't change the fact that if a couple want to marry, they want to be recognised as being married, by the law.
What is being proposed is that this confusion be increased vastly, and whole new categories of partnerships will be legally recognised as marriages, when under Natural Law they are no such thing. Ultimately, we may say that the state has ceased to deal with marriage at all, but will be doling out certificates of 'vaguely committed relationships'.
But I still don't see how anyone seeking marriage would not want their marriage to be recognised as the most committed kind of relationship recognised by the state. And, especially if that is called 'marriage', but even if not, I don't see why they should want to add to the confusion in the social understanding of relationships by having a marriage which is not recognised as (even) a committed relationship by the state.
I have read of a principle in canon law: couples are assumed to be seeking 'marriage as it is, not marriage as they believe it to be.' Thus Anglicans who don't believe it is a sacrament get a sacramental marriage if they intend to be faithful, to have children, and so on. I think we can apply a similar principle to the state, and to society as a whole. Talk about marriage has become more and more confused over the last couple of centuries, but there is something, written on the hearts even of the pagans, which is the truth about marriage. In their confusion, they still seek marriage for the themselves and recognise marriage in others, as it really is. In their confusion, they want to be able to divorce and have a true marriage to spouse number two, three, or four. In their confusion, they want same-sex couples to 'enjoy marriage' too, like everyone else. That, really, is the tragedy of the situation.
Marriage as recognised by the state is not about to become an intrinsically evil thing which we must avoid. Perhaps priests will be stopped from undertaking marriage registrations. But we can't turn our backs on what society recognises as marriage: if we want to work for the restoration of a correct social and legal understanding, such a move would be counter-productive.