You're spoilt for choice in London!!
Here is Truth, and Wisdom.
Smithfield:
Fox and Anchor for some lovely real ales in a beautiful old pub. Was in there earlier! Little alcoves in the back, great for a romantic pint or two.
The Castle by Farringdon tube is another decent pub that's a bit 'livelier', not popular with fogeys!
If you're there around lunchtime, and feel peckish, I can recommend Beppe's Cafe on the corner of Hosier Lane and Giltspur St, just opposite the littleAmbulance station. Pukka little workers' cafe, popular with Binmen and Barristers alike.
Cheshire Cheese, as mentioned by Akira above, is a truly historical olde pubbe. The haunt of Samuel Jhonson, Charles Dickens and others. Actual sawdust on the floor!
Wapping:
Prospect of Whitby, obviously! Oldest riverside pub in the Universe or something like that! Lovely old place. Gets quite touristy, but that's no bad thing. Nice little beer garden to the side.
And my fave, the Captain Kidd. Shame Craig the former landlord has left, but a cracking pub, and popular with just about everyone who's been there with me. Large beer garden to the side, plenty of space for bikes. Like the Cheese, it's a Sam Smiths so a good step up from the usual Fosters/Stella pish.
In all honesty, there are hundreds of good pubs in London. Loads of good ones in the Square Mile alone. Bad pubs are a rarity really. Bad pubs don't survive in a place where people demand high standards.