BTW I'm not sure there's much commonality between the Olympus 593B in Concorde and previous Military but lower thrust versions.
That's correct. The Concorde engine was the Olympus 593B; I believe the "B" was for Big, and it followed the 593D, where "D" was for "development". the B had a larger diameter than the D, and both were bigger than the 22R ("R" for reheat) which was the TSR2 variant.
After the cancellation of TSR2 there had been a suggestion that the aircraft could be used for developing the Concorde engine - but that was too big to fit.