It's a big call, London's best church. But as a bit of a church-enthusiast (if that is even a thing) I think that this is the best church in London.
Featuring in films such as Four Weddings and a Funeral, Shakespeare in Love, The End of the Affair, Amazing Grace, Elizabeth: The Golden Age, and The Other Boleyn Girl, even film people think it is good. It has a very parochial feel, and the streets around it feel like a small village that somehow got eaten up by Central London.
The church itself is very special, and the architecture is fantastic. First built in AD 1123, the church with its great columns is distinct from many other other early City churches. The cafe and bar here are also very nice, and a great pit-stop after a look round the church and surrounding area. They also have Jazz in the Cloister on the second Friday of every month. Have never been, but it sounds nice.
DOWNSIDE: They charge for entry! What would Jesus do? Fairly sure He wouldn't charge people for coming into His church, but there we are. He probably wouldn't have to repair the roof either. Is worth it.
WAP tip: You don't have to pay if you are coming to a service here. The carol service here in December is also tremendous fun.