The highest I have flown on a commercial jet was on a lightly loaded EK A340-500 from Phuket up to DXB on a very clear moonlight night in Nov 2012, and we arrived in DXB about 70min early, and the place was deserted. We cruised at FL43-440 from the start as I recall, with quite a tailwind. I never did the Concorde thing, but have flown in exec jets at that height, and even a little higher, but that is my max for a commercial jet as far as I am aware.
Cheers
Mr Mac