The best club to try is White Waltham (EGLM
www.wlac.co.uk ). Great atmosphere and top instructors. Best way to travel there is fast train to Slough from Paddington Station and then taxi to the club (good local taxi service: 01628 632000 ). Or try a slower train to Maidenhead, which is closer, if you have time to spare.
I am biased because I'm a member there . . . . . but with good reason. Other clubs around London are good (Wycombe, Elstree, Denham, Biggin Hill, Redhill, Blackbushe, Fairoaks, Stapleford) but if you want a good service AND a great bar/restaurant/hospitality etc then EGLM is the one.
There are good bed&breakfasts nearby as well if you want to make the most of your visit.
Have fun