OK, found a link to some trials flown officially ...
Originally Posted by Wiki
In British Airways trials in April 1985, Concorde was offered as a target to NATO fighters including F-15 Eagles, F-16 Fighting Falcons, F-14 Tomcats, Mirages, and F-104 Starfighters - but only Lightning XR749, flown by Mike Hale and described by him as "a very hot ship, even for a Lightning", managed to overtake Concorde on a stern conversion intercept.
Now as I understand the story, it too repeat practice, which was probably unofficial (and didn't need to be as long as the stern intercepts maintained lots of separation). The Tomcat would be flown approximately 80 miles lateral separation and the turn would have to be started well before the abeam point at an altitude and bank which allowed the jet to retain the most energy (shallow) then return to New York.
Next time I fly with the gentleman I am going to beg him to write A&S Smithsonian or a similar repository. Seem like an interesting story which might amuse those who say "nah no way."