Just to be pedantic this law only applies to shops over 20,000 sq feet (ie supermarkets) who can open 6 hours on a Sunday (typically 10.00 to 16.00, although 12.00 to 18.00 is done by a few). Smaller shops like those in Heathrow can open when they want. The chances are, given how busy T3 is in the evening, that the shops will still be open at 20.00. You won't find anything by the time you get to Central London.

You can of course use your Cingular on Sunday night for a few calls, then go to a phone shop Monday morning.