It's probably more the influence of ITAR than any problem on the UK side.
Stocks, magazines, optics, brass and non-pressure bearing parts such as firing pins and ejectors are not restricted here in the UK. The sad thing is, it is easier to fly out with a stock in your suitcase than try to get one sent over.
I declare the item at both ends (TSA on leaving and UK customs on entry). The only hiccup I have had was with cartridge components from one of the crime labs in the US, where the projectiles were unexpanded JHPs. Those were taken for analysis upon arrival at Heathrow but they were released to me the next day.