I started in my 30's on the 737 so nothing is impossible (albeit this was a SE Asian airline) - I quit flying for various reasons but age was an issue but not insurmountable. Naturally, with P2F it is far less an issue (if at all), however, given the alleged shortage of pilots age "standards" will likely slide.
Isn't age discrimination illegal in the UK? If so, I'd imagine that airlines would "quota" to make sure they are within the law, Euro airlines more so (outside of Eastern and Central, can't speak about them).
The bottom line in my opinion though is you'll still be under 40 and given many service pilots also enter at the 38 point it won't be exactly you are the oldest.
Go for it anyway or eternally regret "if only..."