Near Heathrow, I'd recommend easyHotel (between the CTA and Hayes) or the Etap Hotel Hounslow. Have stayed at both at very short notice - the first for £20, the second for £30.

I imagine the problem at the moment is availability, however. A friend's parents have been caught up in this mess on the way to New England, and it took him a good hour of phoning around before he could find any availability - which turned out to be a B&B in Staines.