Ok Iām biased because this is where my āin-lawsā live and where Iām based on frequent trips over. But if you love parks and green space, I highly recommend venturing deeper out into Greater London.
Kew Gardens (Londonās major botanical garden) is so beautiful! Complete with double-decker conservatories (lol why is everything in this country double-decker), peacocks, and a pagoda you just might glimpse from the air if you fly into Heathrow. Itās nearby Richmond, which is a particularly charming lil green and town to walk around in.
I also highly recommend visiting at least one National Trust property while youāre there. Many of the old estates are along the river, so you can combine a museum with being in nature and walking around. So far my favorite Iāve visited in the area is Ham House.
In terms of London proper, one of the most fascinating things Iāve done there is to take an architectural tour of the Barbican, the brutalist mega-living center that sprung up in blitzed out part of the City of London after the war (fun fact this is the center of London and technically considered a separate entity with its own government).
Finally, despite the bad rap it gets, British food is actually quite delicious since itās far more natural and fresher than what we get here. Plus the ācozzy livsā make most food products much more affordable. Highly recommend making use of the high quality fruit and cheese and snacks from your local Waitrose or other grocery.