Absolute closest pool to Heathrow

Crazy idea: I've got a 7 hour layover in Heathrow on two occasions. As much as I like the new T5, 7 hours is a bit much. I want to get out of Heathrow and find a pool in which to grab a swim, ideally making use of public transit and ideally with generous mid-day lap swimming hours. I know of pools out in Reading area, but that's too far. Anyone with any recommendations?