I am a US vaccinated person heading in late August to the Belgium Grand Prix at Spa Francorchamps. My flight arrives in London early in the day. The flight to Brussels leaves at 7 pm. Can I go out and spend the day in London?? I have tried the embassy sites and they make no sense.

As it stands, today, no you can't. England runs a Green, Amber, Red classification for arrival from overseas. At the moment, any country you have been to in the last 10 days has to be on the Green list to avoid some form of quarantine. USA is currently on the Amber list so if you leave the airport you will have to have a test and then isolate in a place of your choosing for 10 days. Also more tests required during that period. This is the UK government page that provides the rules and regulations... https://www.gov.uk/guidance/red-amber-and-green-list-rules-for-entering-england .

Will the rules have changed by the time of Spa (I've always wanted to see the Spa GP but haven't yet made it!), probably. Keep an eye on the web page for updated info.

I know the feeling, had the same chance at Paris, turned into a nightmare getting back to CDG in time. Had already been to Paris and just wanted a fast refresh of seeing the eiffel tower and arc.. Wish I hadnt.

Odds are if COVID did not exist and you had nothing to carry around all day ( could store all in locker at airport but passport/wallet) at best I could see you seeing nearby Windsor Castle.

Flying out of Heathrow is a chaos of different terminals and nothing easy no matter how many times you've been.

If you did store stuff fast, took the express train to London, You might get a 1 loop double deck bus ride and some bad fish and chips.

Any other more optimistic opinions with/without covid?

Don't do it! We did it in Milan and it was a disaster! No time for anything...
Cheers
i

A LONG, LONG time ago, way pre-Covid, we spent a day in London, during a connection time for our flight to South Africa. Took the double-decker bus, everything. It was well worth it. Maybe times like that will come again..