'Mr M', referred to above, probably uses one of the big chains of bookmakers. They operate a machine-based system, purely for their own security. (It has nothing to do with any legal obligations).
Any bookmaker can refuse to pay out winnings without giving a reason, as can firms like Littlewoods who run football pools. Under the Gambling Act 1845, gambling debts are unenforceable in law. If Marlon (in Emmerdale) had been able to keep the betting slip, he could have used it to 'kick up a stink' with the local press but the police wouldn't be able to help him (because the bookmaker hadn't breached any criminal legislation) and he would have no right to sue for his winnings.
Chris