Jack Straw, the MP for Blackburn, now claims to be in favour of same-sex "marriage", which is not, and has never been, the formal policy of his party. If he really has changed his mind, then that is only because he is retiring. He would never have dared face an electorate in which every other non-Muslim was a Catholic, or possibly vice versa, on that basis.
In Scotland, the single most reliable indicator of being a Labour voter is being a practising Catholic. The desire for this whole business just to go away on the part of Labour MPs from there, from the North West, from the West Midlands, and from pockets elsewhere (for example, the constituency in which the largest town is the Vatican City State of Consett, a town increasingly full of Poles on top of the Anglicised Irish) is now somewhere between desperation and despair. Oh, and remember that the SDLP MPs take the Labour Whip.
This thing is never going to reach Third Reading in the House of Commons. Sections of the Conservative Party in both Houses are going to make sure of that. But theirs will not be the greatest joy at that turn of events.