You cannot just file a flight plan declaring an alternate as a UK airport and expect to be accepted there. Heathrow especially is very strict on accepting non - emergency diversions so you would be better off elsewhere and always notify your nominated diversion in advance.
Depending what type you fly, there are several places in the London area to divert to apart from Heathrow eg Luton, Stansted, Gatwick, Farnborough, Biggin Hill, Southend.