As for London itself, what do you plan to see and do outside of day trips? As others stated, London Walks is excellent. I went on the daytime walks and twice on the pub walks which I highly recommend. I have been to London five times and went to London recently in 2018 and 2017 and going back next year for two weeks and plan to see things I have not seen and do some day trips too. I have been to Hampton Court and loved it and spent a whole day there. I was lucky, i went a few days after they had a wine and food festival and the place was fairly empty! I also did not go on the weekend.
What hotel are you staying in, if you don't mind my asking?
I can't wait to go to Kew Gardens as I have not been there yet. Are you planning to go to Windsor Castle, it is a wonderful place to visit and I saw the Changing of the Guard there. I also spent the whole day at Buckingham Palace which was exceptional.
I loved the Victoria and Albert Museum and the Wallace Collection and the Sir John Soane's house musuem. I have not been back to the British Musuem since 2005 and can't wait to see that museum as I really don't rememeber it. I do recommend making a reservation for the Churchill War Rooms they were excellent and saw that museum twice.
Are you going to Greenwich and taking the boat ride up the Thames River and walking across the Tower Bridge, did all three in 2005. Want to do it again next year. I loved St Paul's Cathedral and Westminster Abbey. I also enjoyed the Portrait Gallery, the National Gallery is good but really liked the Tate Britian. The Tate Modern is ok but not a fan of modern art. If you are then it is a must see.
I also enjoyed St Martins in the Field church and have seen four plays over the years in London. Next year I want to see at least two more plays and go to a concert at St Martins in the field church.
I have so much more I plan to see that I have not even mentioned as most everything above I have seen and now I plan to see other stuff I have not seen on this next trip.
There are plenty of museums in London to keep you busy, along with castles, or palaces, Windsor, Buckingham Palace, Hampton court and of course some nice pubs and Selfridges and Harrods department stores where you can have some really nice lunches or dinner.
If you need more ideas on what to see or eat, please PM and I will give you more info.
Have a great time. Bath is lovely too.