Doesn’t the Sky Garden require a timed entry? People also like the London Eye - not on MY list but friends prefer it to the Sky Garden. My favorite museums are the Tate Modern and the Victoria & Albert. Both probably packed in the summer . .
I’ll be there in October before the TransAtlantic on the Dream.
A little if this is to answer your question. The rest is targeted at the OP and anyone in a similar situation.
Sky Garden does have timed entry, too. But it’s free; so, again no $ loss if your travel is delayed.
I wouldn’t pick anything that requires pre-payment.
Another option is a double-decker Hop On Hop Off tour. Usually those can be purchased in line while waiting or perhaps online once arriving in London. Of course, you will have been riding for a while by now.
Tate Modern is not ticketed, free, to the main area (special exhibits carry a fee). Currently (June), it is open until 6 pm.
Giant display of sunflowers (ceramic) at the Tate Modern in 2010. This is modern art.
Afterwards (or before) cross the Thames on the Millenium Bridge, photographing your best album cover pose. Get some walking in. If you continue straight from the bridge, you are at St Paul’s Cathedral.
Statues outside St Paul’s:
Don’t forget Trafalgar Square and its lions (that made a nifty photo).
So much to see, just being in London. A quick internet search says London is the most wheelchair friendly city in Europe, with curb cuts and well-maintained sidewalks. Now, in reality, how an individual’s experience goes could depend on the chosen path.
Seems the recommendation is the bus over the Tube (subway), which may have broken lifts (elevators). Looks like buses are fitted with a ramp.
If you are staying near Kensington, the Victoria & Albert is also free, unticketed.