with a few modifications.
(1) One thing about religion in the UK is that there is much less of a dividing line between Christianity and atheism than in some places. Many people are culturally Christian but don't believe in anything very much. They are religiously indifferent, and don't really care enough about it to be atheists. This is and has been common among our leadership, and makes it virtually *impossible* to tell what percentage of our Prime Ministers were unbelievers - any answer from 3% to 50% would probably be defensible!. Most were culturally Anglican; but many did not have strong beliefs. There are still debates about whether Winston Churchill, about whom more is known than about most Prime Ministers, was a believer or not!
Having said all that:
(2) There is one part of the UK where religion is important and the Religious Right is significant. That is Northern Ireland. A lot of the conflict there is more ethnic than religious; nevertheless, the Paisleyites are certainly genuinely preoccupied with Religious Morality, and for example laws about abortion are much stricter there than elsewhere in the UK.
(3) There is also a version of extreme social conservativism, often though not always linked to religion, that appears in the tabloids and especially in the last few years in the Daily Telegraph. This is linked to economically right-wing attitudes, and increasingly (perhaps since newspapers went online?) to a certain solidarity with American Republicans and hatred of Obama.
(4) Although it is unusual for the religious right to be significant in the UK outside of Northern Ireland, it can happen, and *because* it's not the norm, it's easy to get blindsided by it. If someone had told me in 2008 that within two years there would be a right-wing nut (Andrea Minichiello Williams) getting her 12-year-old daughter to sing an anti-abortion song in one of our local churches; that this church and a couple of others would be encouraging faith healing in the local streets, including people with serious conditions; and, worst of all, that the political pro-life movement would engage in a vile and ultimately successful smear campaign to defeat our MP in favour of a Tory, and that this would then be taken up as an inspiration by other RW pro-lifers - I would never have believed it!!! On the whole, I wish I was still in that state of happy innocence.
(5) The religious Left constitutes a higher proportion of the religious believers in the UK than the USA. Indeed, the upper echelons of the Church of England and to some extent of the Catholic Church here tend to be quite liberal, and are often a nuisance to Conservative governments (they actually tend to think that it's a bad thing to trample all over poor people!) The sort of people whom I've described under (3) and (4) are often explicit rebels against the country's current religious leaders.