Loved our flight on BA1 Concorde in 2003.
The hilarious part was that because of ancient (60's) technology Concorde was delayed almost 5 hours because 1) they couldn't start the only special legacy tractor used to move Concorde to the ramp and then 2) they had a pressure problem with the fuel tanks (ended up being a duff sensor).
We sent the kids ahead on the 747 flight expecting them to arrive after us. We were so delayed they checked into the hotel and were asleep before we arrived.
But the 5 hours in the Concorde lounge was wonderful with all the Pimms, Champagne and strawberries we could handle while watching Wimbledon Tennis. A life moment for sure.
I think they should not reintroduce BA1 until the next SST is flying.