These are the guidelines given in a press release from the Bank of England (PDF) about the new “Adam Smith” £20 note.
What should I do if I think I have a counterfeit note?
Counterfeit notes are worthless. It is a criminal offence to hold onto or pass on counterfeit notes. If you suspect a note is counterfeit, take it to the police as soon as possible. They will give you a receipt and send the note to the Bank of England for analysis. If the note is genuine, you will be reimbursed.
That last sentence doesn’t exactly encourage you to look too carefully does it?