Am not aware of any tours offered that would allow you to see London then return to LHR. You may want to see if you can organise an independent taxi or minibus tour. It's not going to be cheap though, but at least you will get to see something of the city & be assured of getting back to the airport.
Other places you might consider are Stonehenge & Salisbury, or Windosr & Castle which is en-route to LHR. Another idea would be the Historic Dock Yards in Portsmouth, which is really enjoyable if you like history - HMS Victory, HMS Warrior - the first Iron Clad ship, and the Mary Rose - Henry VIII's warship that sank & lay on the bottom of the ocean for almost 450 years.
Yes London is great, but don't limit your thoughts to there, you may find something which makes more use of your time.
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