my uncle is a rather well off lawyer and, when i traveled to london with him, our first night we just went out to a random sushi place right near our hotel, planning to go to a high class fancy restaurant the next night.
this sushi place was so fucking good that we just ended up going back two nights in a row. if you guys like sushi would highly recommend, although it's probably not at all close to berkeley square idk.
it's right near westminster abbey/big ben/parliament so you guys will probably be in the vicinity at some point. it's a small hole-in-the-wall type place. get the soft shell crab maki if you go.
here it is if you're interested.
edit: was probably actually fairly expensive i don't really remember because saké (which btw is pretty good here)