Not do-able in that timescale on public transport. Your journey would be coach to Woking, train to Salisbury and then a taxi to the Henge. Realistically that is 2.5-3 hours each way at least after getting out of the airport. It is possible with a rental car but not exactly a relaxing journey and one that potentially adds some risk to your trip.

Personally I would find something you haven't done in London and enjoy an early dinner too.