my understanding is that Concorde engines are among the most efficient built to date - they had something like 70:1 compress ratio. It is juts the nature of high speed flying that you have to burn much more fuel.
>modern jet engines are so much more efficient
because of high-by-pass. Wouldn't work for supersonic.
From 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."