Just to help a bit,
UK (BAES) builds the aft fuselage, fins and tails of all the variants. They also supply parts of the fuel systems. MB has the seat, Smiths have a fair amount of electrical gear. RR gets all the lift fans, rear swivel nozzles and the roll posts for the B variant. Probes for the B and the C from Cobham.
I believe that total UK share a few years ago was around 12% to 14%. However, these figures will already be out of date. Any figures will be less than exact, but at the time I was around the programme, for the SDD phase UK plc had already got about $10bn worth of work for a Government spend of around £2bn.
I'm not trying to argue that anything is free here - but F-35 is not the worst deal the taxpayer has had, so far.
Best Regards
Engines