Plus, you're forgetting another big one. The SR first flew in 1964, the Concorde in 1969. The SR was faster, and built 5 years earlier. The Concorde very likely built on lessons learned from the SR.
Actually, you've got it the wrong way around.
The Concorde built on lessons learned from the *British* aircraft and (especially) jet-engine industry, which was world-leading at the end of the war and towards the 1950s. E.g. Concorde draws heavily from experience building the TSR-2. Concorde's engines were *directly* based on the TSR-2's Bristol Olympus engines, which draw heavily on mid-40s Bristol engine technology.
The US had to licence designs from the British to learn how to build jet engines. A number of different British engine designs, from the original Whittle engine, to later Bristol, Armstrong-Siddely and Rolls-Royce designs, were licensed to a number of US makers, including Curtiss-Wright, General Electric and Pratt & Whittney.
It would be far more fair to say the SR-71 drew from British aircraft industry R&D.
NB: I'm not British, and I don't have any great reason to talk up Britain over the USA.