Ari,
Agree with Tony your best bet for one round is SW London, outside the M25 belt.
If you've one round I highly recommend Woking GC. You can get a direct train from Waterloo to Woking, then grab a taxi to the course.
Contact the club secretary, George Ritchie, and explain you are into golf course architecture, and he probably will have a sympathetic ear for you. And we've been experiencing drier conditions as of late so it might hold out and offer some fine surfaces.
RT