And the SR-71 would still likely beat Concorde if takeoff and landing was included (from KJFK TO EGLL), but it wouldn’t be as big a time difference. The Blackbird would probably immediately refuel after takeoff (they takeoff with a light fuel load normally), while Concorde can go pretty much flat out right away if cleared to do so (which I think it did going from NY).
There is no "probably" about that initial refuelling, and I believe that overall the contest would have been a wash.
The SR-71 couldn't reach anywhere in Europe even subsonic without reheat, hence I strongly suspect that in-flight refuelling occurred a number
of times, not just immediately after take-off. Those J58s are going to drink fuel at an alarming rate on full bore. But in principle you are correct in that the SR-71 certainly refuelled just before
accelerating past New York, in order to exclude that first slow-down.
For example, in 1971 the SR-71 was awarded both the Mackay and Harmon Trophy for a much longer flight, clearly involving deceleration for multiple refuellings, and consequently the average speed was considerably reduced to "only" 1428 mph.
Applying that figure would immediately extend the NY-London time to 2hrs25mins, and yet still not include fair allowance for take-off and landing.
The SR-71 NY=LON record flight began and ended with supersonic flight thru' imaginary gates at 80,000 feet over NY and London (the effect of sonic booms being mitigated by the extreme altitude). It might not have been at Mach 3 in both cases, but lower transonic speeds were certainly possible even over such built-up areas.
In contrast, Concorde didn't just have to slow down on final
approach to Heathrow, but would already have to slow down to subsonic speeds 450 miles out as soon as it crossed the Irish coast (or adopt a longer more southerly routing, but reducing speed well before reaching the Bristol Channel, still 250 miles out from LHR)
[Technical note; SR-71 data isn't always easy to find, but an SR71 at Mach 3 at 80,000 feet is only generating 43% sonic boom pressure compared to Concorde at Mach 2 at FL480. Indeed, there comes a point where high altitude sonic booms become inaudible at ground level. Unfortunately Concorde was too large an aircraft to ever enjoy that luxury.]
Nothing to see here; move along please.