You might have a lok at this; Anselm Franz who designed the Jumo 004 of the Me 262 also designed the engine of the M1 Abrahams tank and the UH-1 Iroquis Helicopter after he immigrated into the US.
http://www.memagazine.org/backissues/september97/
features/franz/franz...
There were a number of factors; primarily was the fact that the Germans were short of Nickel and Chromium. When the Prototypes of the Junkers Jumo 004A came out that powered the Me262 the turbines, combustion chambers and exhaust nozzle was out of pure nickel chromium alloy.
The Production Jumo 004B engines had: 1 Austinitic Steel (Stainless Steel) Air cooled Stainless steal blades ionstead of solid refractory alloy blades. These didn't last long.
Changing the material also changed resonance and the Germans had to redesign the engine and run the spools at 8700 rpm instead or 9000. (they used musicians to pick the harmonics)
2 Combstion Chamber of Aluminuim Oxide Coated mild Steel. this was prone to burning through.
3 The translating exhaust cone nozzel was also of steel and distended and fell of sometimes blocking the exhaust and causing a flame out.
British engines didn't have the refractry alloy problem to deal with. Additionaly although the first German engines used centrfugal compressors they concentrated on axial flow types for the Me 262 because of a perceived superiority in efficiency and lower frontal area. Such compressors are more prone to surging and choking and require more sophisticated control or gentle throttle handling and it took the Germans a while to perfect these control systems.
For some resason the Germans also used a 10hp two stroke to start their engines, this was a pain to opperate (even thoiugh it had their own elctic starters) compared to the british all electrics. I don't know why; perhaps it was to do with Lead or Battery production? I note that the Fw190 had its electric control repaced by hydraulics as the war progressed and that the Germans always had a inertia flywheel starter crank on the Me109 to spare the battery/
I think it is fair to say that material shortages not ingenuity delayed the German Jets.