Actually the fuel efficiency of Concorde in "max cruise" auto pilot mode (aka max speed) is way better than people think: it didn't fly with reheat on (that's what is called supercruising in military planes). Reheat (aka afterburners) was applied from Mach 0.95 to 1.7 and for taking off.
The hourly flow rate in supersonic is roughly the same than in subsonic (cruising speed was around Mach 0.9), something like 20 metric tons per hour.
So the faster you went supersonic, the better as your fuel efficiency would increase.
For example, Concorde cruised at Mach 2.05 with its engines giving an SFC of 1.195 lb/(lbf·h) (see below); this is equivalent to an SFC of 0.51 lb/(lbf·h) for an aircraft flying at Mach 0.85, which would be better than even modern engines; the Olympus 593 was the world's most efficient jet engine.[2][3] However, Concorde ultimately has a heavier airframe and, due to being supersonic, is less aerodynamically efficient, i.e., the lift to drag ratio is far lower. In general the total fuel burn of a complete aircraft is of far more importance to the customer.
The overall thermal efficiency of the engine in supersonic cruising flight (supercruise) was about 43%, which at the time was the highest figure recorded for any normal thermodynamic machine.[3]
The hourly flow rate in supersonic is roughly the same than in subsonic (cruising speed was around Mach 0.9), something like 20 metric tons per hour.
So the faster you went supersonic, the better as your fuel efficiency would increase.
There's even an entry about that in wikipedia: https://en.wikipedia.org/wiki/Thrust_specific_fuel_consumpti...
For example, Concorde cruised at Mach 2.05 with its engines giving an SFC of 1.195 lb/(lbf·h) (see below); this is equivalent to an SFC of 0.51 lb/(lbf·h) for an aircraft flying at Mach 0.85, which would be better than even modern engines; the Olympus 593 was the world's most efficient jet engine.[2][3] However, Concorde ultimately has a heavier airframe and, due to being supersonic, is less aerodynamically efficient, i.e., the lift to drag ratio is far lower. In general the total fuel burn of a complete aircraft is of far more importance to the customer.
And on the Olympus page: https://en.wikipedia.org/wiki/Rolls-Royce/Snecma_Olympus_593
The overall thermal efficiency of the engine in supersonic cruising flight (supercruise) was about 43%, which at the time was the highest figure recorded for any normal thermodynamic machine.[3]