Had a wonderful time several years ago at St. John. Pretty unique restaurant if you want something that is truly English and not just internationally styled.
Ledbury.
Its been ~18months ago but we loved the Ledbury and would certainly recommend it! We went to Dinner at Heston Blumenthal and like Ramon above, it just didn’t thrill us but it was certainly good. Our experience and Gordon Ramsey was the best of our trip. So, my opinion of that differs, I guess, from the OP’s search.
JD
Another option if you really want to focus the dinner on wine would be getting someone to host you at 67 pall mall. Food is very good, if not Michelin star level, but wine list is insane, both in scope by the glass and attractiveness of the pricing. Glasses of stuff like 70 latour from mag, 64 la tache etc etc anyone? You may be able to call them and ask to try the club out as you’re considering becoming an overseas member.
Another vote for the Ledbury.