If it's worth claiming (either fund wise or spite wise) have you checked to see if you can file a tax return and if they'll accept one. From what I've read about proof of earnings for the UK, it looks like the second most document that's used for things like this (the first being letters of proof from a person's employer).
That’s correct. If the amount worth it then he could probably go for notarised documentation duly signed by legal representative. This is also one of the solid proof for such work and it adds up the legality since it is witnessed in front of the legal which is far more strict.
At least in my country that would be far better proof. When it comes to the employer proof well that can mix up with your personal life a bit and everyone might get buzz that we gamble and shit. Just making point here nothing else. If OP really wants to get over this then they have to follow the stake rules I guess.