Have a look at AW and other websites. there plenty of flats in hounslow/harrow/Wembley and other areas.
Depends how much you want to pay and your desires. If you ever never done a punt at all I would say that it is not a romantic encounter or at least rarely. Why not try a walk up in soho and see if how it goes. At least if it goes wrong you will not waste too much dosh.
The best punts I have had were overseas. Cheapo weekend in Prague ?
ps stay away from street girls