A US airman's certificate is valid in the UK for day/VFR private flights in G- registered aircraft.
White Waltham is a great club, just on the western edge of Heathrow's class A control zone.
Another alternative is Headcorn in Kent, which is home to the
Tiger club and near a main-line railway station. They are not too far from the white cliffs of Dover if you're after a bit of nostalgia (but watch out for the Hun-in-the-sun!).