Carrying less fuel obviously has many advantages for the entirety of the flight in all phases.
Actually what would probably save the most fuel in the London area would be for Heathrow to pour some concrete and build a third runway! Sorry, I could not resist. I am paid by the hour so it matters little to me, but I recently read that there is almost 200K pounds of extra fuel burned per day at LHR in the various holding patterns. Oh, sorry again, I forgot that Boris is going to start the concrete pour in the Estuary