And nip down the road to the Textile Museum where the Biba exhibition has just opened. They advise you to book.
(I would also ask around friends to see if anyone can lend you their membership cards for places like the V and A, Tate or the Royal Academy, or an Art Fund card. I know it’s naughty, but my reasoning is they need to prove footfall for funding, you will probably also buy something in the shop or cafe so that is money they are getting on top of the membership cost.)
Another great place for an adult mooch is Marylebone High Street, great indie shops and cafes, a world famous bookshop, close to the Wallace Collection, nice little park to sit in with award winning toilets.
If you have never been then Greenwich is a lovely place to visit. The Observatory, The Painted Hall, Greenwich itself. You can get there on a river boat ( not a tourist boat) which is a treat in itself.
Chelsea Physic Garden is another good call, tie it in with a trip to Peter Jones in Sloane Square, less hectic than John Lewis, go to their cafe on the fifth floor and try to get a table by the H U G E window, amazing rooftop views. There is a good little shopping area opposite called Duke of York Square.
if you have a rainy day then the Barbican is good , sadly the Museum of London is closed atm, but they have an art gallery, there are often lunchtime concerts, comfy cinemas and it is under cover.