If what you're looking for is stuff that you can get in any major UK shopping district, then there are several places other than Central London that are convenient to Heathrow and may work.
For instance, the Travelodge in Kingston is offering rooms that night for £39. It's a short walk from both the train station and an express bus to Heathrow (the X26). And the center of Kingston has every British chain store you can imagine. You may even be able to check into your hotel, do the shopping you want, then go into London on the train for an evening if you prefer.
The X26 takes about 45 minutes from Heathrow to Kingston bus station (just behind the Travelodge) and costs a standard London bus fare (£1.60 if memory serves). Note that London buses don't take cash, so you'll need an Oyster card, but you can get one at Heathrow.