Re: Turkey is a NATO country.
Having done some research it looks like Turkey is just the first place in Europe to build an engine overhaul facility, Norway and the Netherlands are due to have one each on line by ~2020 as well. There's an anticipated need for 3 overhaul lines in the Europe region and countries bid to host one, on the grounds that it's about a $1B investment for the country involved. So it's entirely possible we'll be shipping the engines across the North Sea rather than to Southern Europe.
I don't think there's anything to stop the UK doing all its overhaul work itself, except for the substantial investment involved.