BEagle.
Fixed Wing Fast Jet Flying Training is delivered very well by the RAF, with RN input, on behalf of defence and there is no reason to change that. Except we're changing it to MFTS apparently.
I am unconvinced myself of the requirement for any UK based fast air training for the F-35C given the USN and French make do with T-45C and as far as I have heard MFTS aren't looking at a big under carriage and a fresnel lens with which to practice flying into the ground in a nose up attitude and calling it a landing.
Therefore we actually need to send our small cadre to the US anyway. This leaves EFT and BFT for the UK.