The 285 bus (24 hours a day) from Heathrow goes past a decent sized Tesco (called 'Dukes Green' IIRC) on the way to Feltham, the bus connects to Feltham railway station and there is an Asda right there. Think the Tesco is even an annouced stop on the bus displays, but it is hard to miss if you keep a look out.
(There is also a Lidl close to the station as well.)
Feltham station is zone 6, and the 285 is inside the London Busses area, so covered by normal ticket rates / travelcards / oyster price caps.
Both the Tesco and the Asda are open 24 hours a day (obviously only until midnight Sat with limited hours on Sundays due to trading laws, opening monday 6am, otherwise 24 hours).
EDITED TO ADD: The 90 and 490 go past the Tesco as well, the 90 doesn't come into the station at feltham but goes down the highstreet, this just as easy (or easier) for Asda, but less apparent when you have arrived.
Last edited by David-A; Jan 12, 2011 at 7:48 pm