Let's suppose that in 1939 the Air Ministry decide that the various very high power piston engines, Bristol Centaurus, RR Vulture and Napier Sabre are proving to be more trouble than they are worth and put their faith in Dr Pye's recommendation of Sqn Leader Whittles new engine. Then they put Power Jets into the hands of Hives at RR instead of Rovers.
The use of Rover to develop the engine in OTL put back the entry into service of the engine by over eighteen months at least.
Then instead of getting Gloster, a company whose last design was a biplane! to design the first jet powered aircraft for the RAF the best designers in the industry are commisioned to submit designs.