>>> And you MUST go to Cecil Court, a small street with two dozen antiquarian book stores, it's amazing. <<<
I still have much of the stuff I acquired "unwillingly" ( too tempting) in the past - some beautiful prints with an antique patina to them
Don't forget to go to some of the flea markets - there is a small one at Covent Garden and of course there is Portobello.
Also, if you are going towards end of June, that may coincide with the Wimbledon fortnight. Hotels may be a bit less available, or if they are, they could be at peak rates.
Re food -- Harrod's Food Hall is very well-known...but not too many people know that they serve a sumptuous buffet in their Georgian Restaurant on the top floor. The food and the ambiance are worth the price. If you are on Piccadilly Circus ( roundabout

), there is an excellent continental cuisine restaurant in the area called THE CRITERION ( owned by famous chef Marco Pierre White), which I seemed to have recognized in the latest Russell Crowe movie called A PERFECT YEAR. It's a nice place to celebrate being in London. Not too far away is Soho and the Chinese restaurants - usually but good food and very close to the the theatres ( some of which are actually close to or almost in Soho).
And don't forget to look right when crossing the street