What are your must see pubs in London?

You ask "must see" rather than "must drink at".

Are you looking for iconic architecture and fit-out or best foods or best drinks?

For beautifully tiled and quite different I like the Black Friar at Blackfriars.

I agree with Nigel’s recommendation of The Black Friar. While a bit touristy, Ye Old Cheshire Cheese in The City makes for a sublime lunch stop (it was rebuilt in 1667). Other older, historic pubs I found to be nice include The George Inn, The Counting House, Lamb & Flag, The Grapes, and The Mayflower. Also, while it may have a few too many tourists due to the fact that it is just a block off of Trafalgar Square, I enjoy The Lord Moon of the Mall, as it has one of the best selections of beers on tap/cask in London IMO.

I liked The Surprise in Chelsea.

For a tongue-in-cheek photo opportunity you can't go wrong with a selfie taken
in front of the sign for The Spread Eagle.

There are more than one establishment with that title, but the particular one in East London has an all-vegetarian menu and welcomes alt lifestyles. The others are all cute in their own way, though.

The Churchill Arms in Kensington near Chelsea is nice if you like flowers. Not many pubs have entered the Chelsea Flower Show...

Of all the pubs I visited, my favorite and most memorable was The Holly Bush in Hampstead.
A long block from the Tube Station.
It felt like a cross between a fine dining restaurant and a local's pub. Good chance you'll be the only non-resident in the place.
They had a few true cask ales when I was there (more than a year ago).
I'm sure there are a lot of places like this around London.

http://www.hollybushhampstead.co.uk

You may want to go on a pub crawl offerred by the London Walks. I went last year and had a great time. I did the Hempstead Pub crawl and we went to three pubs ( including the Holly Bush which is really nice) and did a walk around the area. The guide was great, the area was like a charming village and you did not feel like you were in London, and they leave you right near a tube station.

This way you get to see pubs you would not normally go to. I am going to do that again this year while in London. At least one if not two. They start around 7 or 7:15PM, they have a web site which will explain it all.

I also liked the Counting House.

Nigel’s and my favorite The Blackfriars. Over by the Wilton Music Hall, the Princess of Prussia. In Rotherhithe The Ship. In Highgate, The Wrestlers. By Royal Albert Hall, The Queens Arm.

Echoing Jay, Ye Old Cheshire Cheese is lovely. Just don't stay on the ground floor, start walking down the stairs . . .

If in the Kensington area, The Hereford Arms has good food and drink and is a two-block walk from the Gloucester Road Tube station. Huge Sunday roast meals at the mid-day (reserve). It's a Fuller pub but sometimes has craft-style beers too. http://www.herefordarms.co.uk/

Yes the Blackfriar is worth a trip just to see its playful decor. https://www.nicholsonspubs.co.uk/restaurants/london/theblackfriarblackfriarslondon