It was a Lightning that intercepted Concorde from behind:
English Electric Lightning Site - Story of the Month
I was in the Air Training Corps in Bristol in the late 80s and flew in the Chipmunks based at Filton. Used to see the spare Concorde sitting there outside the hangar. My father worked at BAe so we would go to the open day and see Concorde do her stuff there.
And a question of my own - I've heard that the engines were pretty powerful even at ground idle, so powerful that if all 4 were running then a tug would not be able to push her back. Any truth to this? Were just 2 started, pushback and then start the remainder? Also heard that the pilots had to watch the brake temps whilst taxiing out to takeoff - was this also due to the power?