You are quite right and GE do indeed produce excellent areo engines but is it not true that the UK government agreed to assist the USA in this field by giving them (I believe) technology from the Derwent engine ???
Don't forget that Rolls-Royce has had an even more spectacular growth since 1971 with the RB211 family. Prior to that, it only had the Spey and Conway in limited numbers and applications and did not compete with P&W or GE. More importantly it has achieved this as a relatively small business without benefit of the massive USA defence programmes.
NB. Yes I know about the company going into receivership and the takeover of Allison.