We don't have the separation of church and state, so we have an official national church - The Church of England. They basically practice an extra-mild Christianity. In theory the closest American parallel would be the Episcopal Church, but the CofE is arguably closer to the Universal Unitarians. They don't really hold a strong position on much of anything apart from being nice. Most people in this country aren't particularly religious and only a tiny percentage are regular churchgoers, so most of our churches try very hard to be accessible to atheists and agnostics. The church has almost no political or social influence despite being deeply embedded in the establishment, because very few people are interested in what they think.
This interview with the Archbishop of Canterbury (the head of the Church of England) might shed some light.
We do have a variety of other churches. There's a significant Methodist tradition here, a smattering of Pentecostalists and Baptists, but the only churches that are actually growing are foreign-influenced Evangelical churches and Mormonism. The major Evangelical churches are strongly influenced by American Evangelism (although they tend to be less vocal about things like abortion), but the racial aspect is very different. We didn't have slavery, so nearly all black people here are immigrants or the descendents of recent immigrants. In major cities, you'll find dozens of different churches of various nationalities - Polish, Romanian, Congolese, Ghanaian, Angolan, you name it. There aren't really "black" churches as you'd recognise them in the US, because there isn't a singular black culture.
In London inb particular there are also a few wealth doctrine cults. They are a disgusting American import and seem to be mostly popular in the black community.