Few things.
They won’t be working mil controllers from 56N 10W over the Lake District and North Yorkshire if they are going to the Middle East or Germany. They would get in the way of the civil traffic too much so the civil controllers work them.
There is no mandated way to route to the Middle East or Germany when routing that way. The shortest way, given the present route structure, from 56N 10W to the exit of UK airspace via WAL and MCT is via the Lake District and North Yorkshire. They then route overhead Amsterdam and into Europe.
I’m sure that if civil aircraft are asked if they could accept direct routing then the USAF is asked as well.
Lastly, why does the USAF deserve preferential treatment with better directs in UK airspace than all of the other flights that are also in a hurry? UK atc does its best to give everyone a good service including directs whenever possible. Quite frankly UK atc does not give two hoots about the USAF being in a hurry.