1. Ye Old Mitre.
Built in 1546, apparently Queen Elizabeth I danced round their indoor cherry tree (its remains are still preserved there) and it was featured in Snatch. It is not considered part of London but part of Cambridgeshire, something to do with Bishops and walls. Closing time is at 10pm as the gates at the end of the alley are locked then. I saw it on a programme about Samuel Johnson and his dictionary; he lived nearby and they claim him as a past local.
1 Ely Court, EC1N 6SJ.
Directions (varying- seems it's hard to find): Nearest tube: Holborn.
Entrance via passage off Hatton Gardens, behind NatWest or via Chancery Lane Tube Station, walk down hill to Holborn Viaduct, turn left into Hatton Gardens, cross over to the other side & pub is at the end of the alleyway, to the side of number 9 Hatton Gardens (Hirsch the Jewellers).
**UPDATE TO THIS**: Visited in October and actually it was really busy and full of yuppies as it's right in the middle of the banking bit. Not a lot of atmosphere and very crowded. Bit of a disappoint really...
2. St. Bartholomew the Great church
The top one is the gatehouse, which the only bit I saw on New Tricks, but that was enough. It seems the inside of it is famous too- it was in Four Weddings & A Funeral, Shakespeare in Love and even The League of Gentlemen Christmas Special. It was founded in 1123 as a priory and is supposedly the oldest place of worship in London, after the Tower of London (people worship there?). The reverend there has so many letters after his name you'd need three sheets of Letraset to spell his full title on a folder.
It's also just round the corner from #1- what a convenient coincidence.
6 Kinghorn Street, EC1A 7HW.
Nearest tube: Barbican.

