Assuming that your flight is on time, as has already been stated, it will take at least an hour to get through the airport. If you are heading to the States, the recommended check in time is 3 hours before the flight and 2 hours if travelling to Europe and 4 hours if flying to Israel.
Will you have luggage? If you have to use the left luggage facility at Heathrow, this could add another half hour to drop and collect.
The Heathrow Express is quick, but it terminates at Paddington, which isn't that helpful if you want to see the sights! You will then need to get onto the Underground. If you were to head to say Westminster (for the Houses of Parliament), this takes the same time door to door on the tube vs the Heathrow Express and involves only one change (two on the HE). Tubes run more frequently than the HE. I would allow an hour to get back to Heathrow.
It's too early to check if there would be any engineering work on either the HE or the Underground, which, being a Sunday is possible - check tfl.gov.uk website closer to your travel date for info.
Shops have their opening hours restricted on a Sunday - most open noon - 6pm in central London, but some are 11-5 pm. Cafes and restaurants are not restricted.
You may have something like 2.5 hours actually in London - time to walk past Buckingham Palace, the Houses of Parliament, Trafalgar Square, grab lunch and pop into the National Gallery or Covent Garden. This all assumes that your flight is on time....