In a word: No.
Smoking areas | Heathrow
Heathrow is a smoke-free airport, in line with British law on smoking in enclosed public spaces.
Smoking is permitted in designated areas outside the terminal building.
However, please be aware that once you have passed through security control, you will not be able to smoke anywhere in the departure lounge.
If you are catching a connecting flight at Heathrow, please note that smoking is not permitted during the connection process. It's only possible to access the outdoor smoking areas by entering the UK (via passport control), and you would then have to pass through security control to return to the departure lounge.
Electronic cigarettes
Passengers are not permitted to use electronic cigarettes within our premises. Where you are intending to carry cigarettes in your hand luggage, please check with your airline to ensure they are allowed on board the aircraft.