Suggest that you Google Heathrow Hotels and check out the upmarket ones with a gym - there are plenty within striking distance of T1,2,&3 (by bus - Hoppa costs a few pounds return), T5 Sofitel is about the only option unless you catch a taxi out to the Runnymede Hotel (classy place about 15-20 minutes from T5 - they may run a shuttle). Hilton at T4 is about the only option. Last time I tried this as neither a non resident nor a 'leisure club' member the hotel in question was very reluctant to let me in. They cited 'health and safety' liability as the reason even when I offered to pay an extortionate daily rate. Probably worth a call in advance to set it up and to avoid the argument.