Need to find a hotel for tonight close to the Heathrow Airport. Hilton and the Sheraton are booked. Any help would greatly be appreciated.

Check Renaissance Heathrow.

I would go on Priceline and bid for a 4* hotel, or go to Hotwire. You should still be within the time limit.

We have stayed at the Jurys Inn at Heathrow. It's actually about 5-10 min easy flat walk from Hatton Cross tube station. Hatton Cross is one stop away from Heathrow.
Kay

If the hotels within the airport perimeter are full, there is the Continental in Hounslow which might be available, near Hounslow central tube. It's quite a nice hotel with a Gold's Gym and swimming pool

We also stayed at the Jury's at Heathrow. It was an easy walk from the Hatton Cross tube station. I would stay there again in a heartbeat. I don't know all the names of the tube stations but we caught the tube and went into London for the day. We took the hotel shuttle the next morning back to the airport.