About London . . .

The London Silver Vaults (Chancery Lane station) if you enjoy beautiful antique and contemporary silver, with dozens and dozens of shops in the underground vaults.

https://silvervaultslondon.com/

Take a London Walks tour or go by yourself to Greenwich going one way via Thames ferry.

Climb to the top of the London Monument-erected to commemorate the Great Fire. I believe it's only a couple of GBP to climb the 300+ stairs, you also get a certificate saying you climbed to the top.

London Transport Museum

Museum of London

Globe Theater, Victoria and Albert, Tate Modern, concert at St. Martin in the Fields, Natural History Museum, Museum of London, Kew Gardens

We are taking several walking tours with London Walks www.walks.com (going to Hampstead and one on the Southbank) and New Europe Walking Tours https://www.neweuropetours.eu/london-walking-tours/ (the Westminster area.)

Something to consider...

Imperial War Museum and/or Churchill War Rooms if you like WWI/WWII stuff
Tate Modern if you like modern art
Harry Potter studio tour if you're into it
Windsor Castle

Much good stuff here! (But no reason to stop now. LOL)
Never knew there was a "Silver Vault"! I'll take a look at that link. Thank you.
The Greenwich expedition sounds interesting too. And I have heard the V&A is fun.
We did already arrange a tour and a performance (Merry Wives) at the Globe for this trip (right wavelength!). And with Chihuly installation at Kew, we were looking to do that as well. Museum of London looks like it might be good as well as the Churchill War Rooms.
We have done a London Walk before and thought it a bargain, so we will probably squeeze that in as well.

You've probably got enough to go on but....

• Sir John Soane's Museum

• Wallace Collection

• British Library

• Apsley House, home of the Duke of Wellington, victor at Waterloo

• RAF Bomber Group Memorial in Green Park - very moving

You can add them to your never-ending list of "Things to do next time in London", hahaha!

Museum of London-you can see part of the old city wall.
Bletchley Park is on my bucket list.

If you go to the London Silver Vaults continue down Chancery Lane and take the secret passage through to Lincolns Inn shhhhhh. Take in a drink at the Seven Stars because it's just the cutest pub ever, and then swing by the Royal Courts of Justice to see it's impressive facade. You could then continue down Fleet Street stopping off at Ye Old Cheshire Cheese. I would then continue down to Ludgate Circus remind you yourself how magnificent St Paul's is and then cross over the Milennium Bridge to Tate Modern.
Also book ahead for tickets to the Skygardn (it's free).

Take a trip on the Canal to Zoo or Camden Market.

http://www.jasons.co.uk/

https://www.londonwaterbus.com/

Other suggestions: https://secretldn.com/free-things-to-do-london/

If you enjoy good, inexpensive food from around the world; literally hundreds of different outlets specialising in a few authentic dishes each... a day in Brick Lane (Sunday is best) and Spitalfields Market (any day) is highly recommended. There is more to those areas than just food if you want to explore further. Street art and vintage fashion, knick naks and bits and bobs feature too.

a ride on the Post Office Underground.

visit a hidden Tube station.

walk under the Thames.

visit a roof garden. or ten.

The Museum of London, it presents a chronological history of the area. I don't think it gets the credit it deserves. We enjoyed it much more than the British Museum. You said that Hampton Court is on your list-great choice. It's a toss up if it or the Tower of London was our favourite.

Day trip to Windsor, tour the castle and St. George’s Chapel. Take train from Paddington Station to Windsor-Eton Central.

Sometimes I see posts here asking: "How much time do I need to allot to London?" Once again, you all prove that my usual response (whether I post it or just think it) to that question ("One can never have enough time.") is not far off the mark. Thank you all.

Had not thought about Brick Lane market - and since we have a Sunday that might be perfect. The post Silver Vault walk suggestions are great too (though we did visit Ye Olde Cheshire Cheese on our earlier sojourn and also did a cursory swing through the Inns (busman's holiday, I guess). We spent a New Year's Eve (well, the stroke of midnight, at least) on the Millenium Bridge - great memory.

Again, these are a lot of great ideas. Thank you!!

Agree with Brick Lane and the Spitalfields Market (note that there are two - Spitalfields and Old Spitalfields - across the road from each other).

While on Brick Lane, look in at the Beigel Bake (yes, that's how they spell it). Like Katz's in New York or Wilensky's in Montreal, it's a bit of the old Jewish neighborhood that remains as the area has otherwise completely changed. Like them, you get "dinner and a show" as you see the way the staff interacts with the customers (in all three cases, food is secondary to the total experience). And like them, you see a true cross-section of the city patronize it (it's open 24 hours, so it gets everyone from clubbers to pensioners lining up for sandwiches, desserts, etc).

While the art in the Tate Modern is a mixed bag, if it's a clear night, the view from their tower (free) is great.

Look at the list of covered attractions for the London Pass. While I didn't get one, that's how I learned about the Museum of Brands, Packaging, and Advertising, and the London Jewish Museum. Both were very worthwhile, and as a bonus, got me to neighborhoods I wouldn't otherwise have seen.

By taking Rick's City walk, I went to the Inns of Court area. It's very interesting - pin-drop quiet, as well as looking just what I expect "ye olde London" to look and feel like (intermixed, of course, with newer buildings).

Harold, i didn’t know there were two, a search does show Spitalfields and Old Spitalfields markets but they show in the same location. Can you give some advice on how i find the other one as i’m in the area most weeks. The Spitalfields Market as i know it is between Liverpool Street tube and Brick Lane; its the covered area with the ‘goat on boxes’ at one end. Is there another one? Thanks.