There is a very nice/posh restaurant IN the British museum. But I don't think it will work for you.

Have a layover in London...arriving Heathrow around noon....leaving the next morning. We've been to London's tourist places but need an idea for lunch and "something." Lunchin the same neighborhood as the "something"???? Someone suggested a walking tour....lunch at Launceston Place in South Kensington??? We haven't been to the British Museum. Are there tours inside the museum? We will have a little jet lag so don't want to have to do a lot of thinking (!!)...........Shopping is okay but only interesting shopping (not into buying clothes).
If you haven't been to the British Museum there are obviuosly a lot of tourist new york city bus tours from washington dc sights in London that you haven;t seen. But depending on if yuor plane lands on time and if you have to go through new york city bus tours from washington dc Immigration - by the time you get into London you might not have a lot of time for the Museum after getting something to eat.
There is a very nice/posh restaurant IN the British museum. But I don't think it will work for you. W/ a noon ETA, by the time you go to your LHR area hotel, check in or drop the bags, return to LHR to catch the tube and ride to the museum it will probably after 3PM. On Mondays the museum closes at 5:30 and the restaurant only does afternoon teas.