Activity ending at noon

Walk along the Thames Path to the Garden Museum.

Or visit the Saatchi Gallery and then see if you can still visit the cafe on the grounds of the Royal Hospital. Loved the gift shop there.

The Tate Britain is within walking distance of where you are staying.

I usually take an afternoon flight home from London. I generally go for a nice, leisurely breakfast at a restaurant (Dishoom and Nopi are two I like) and then for a walk. I prefer to walk outside rather than visit a museum as I will be cooped up in a plane for 8 hours. You could take a walk along the South Bank of the Thames or the Flower Walk in Kensington Gardens.

I should have mentioned my date for which I made the inquiry, this coming March 14. I would think gardens might not have much to see in late winter. Am I correct? I enjoy gardens, but in Iowa I would not bother going in mid March.

In mid March I would personally expect Kensington Gardens to be a riot of spring colour.

The Tate Britain is within walking distance of where you are staying.

There is a special exhibit at the Tate Britain right now consisting of 60+ paintings by John Singer Sargent (runs from Feb. 22 through July 7). I will be heading there the week of March 18th and am really looking forward to seeing his paintings. https://www.tate.org.uk/whats-on/tate-britain/sargent-and-fashion? Definitely something you could manage on your last morning, and well worth seeing.

ETA: I don't know about this year, but these two videos of Kensington Gardens from March 2021 and March 2022 do not show a lot of flowers; mainly some daffodils and a few other early spring bulbs. That's not to say it would not be an enjoyable walk, but I wouldn't expect a ton of flowers.
https://www.youtube.com/watch?v=4jgKTm71Ggs&ab_channel=ShiranDeSilva
https://www.youtube.com/watch?v=l3xL8O-jSpo&ab_channel=Pinkybelle%E2%80%99sAdventures

I live somewhat north of London but I visit frequently and am a member of Kensington Palace so like to walk in Kensington Park. I too would be surprised at the Ides of March to see much more than daffodils - snow drops and crocus mostly gone over - and some hyacinths. I'd be happy to be proven wrong - I like flowers, especially this year with such a warm and very wet February.

Some of the glass houses at Kew Gardens may something.

I note that the tulip festival at Hampton Court Palace runs well behind the Keukenhof in the Netherlands, not opening until 15th of April.

will you have been to visit the Wallace Collection https://www.wallacecollection.org/ ? It opens every day at 10. Free. Lots of really good stuff there.

We walked in Kensington Gardens on March 14 last year. I know the exact date because I spent part of our time that morning sitting on a bench in the Italian Garden filling out an online claim form for the iPad my husband left on the British Airways plane when we arrived at Heathrow the previous day. (Yes, we did recover the iPad eventually).

We entered from Bayswater Road through the gate at Brook St. and walked past flower beds under renovation for spring, which was interesting to see. . I do not recall anything in bloom in the Italian Garden, but we walked around after completing our claim form task and found a few groups of early daffodils—the little ones—-but that was about all. It was a great place for birding, though, and we always enjoy seeing dogs at play with their people.