The relevant legislation is the Gambling Act 2005.
It is difficult to be able to advise with any certainty without knowing exactly how the betting scheme is intended to operate and the number of potential punters. On the whole, however, there are a wide range of exemptions from the requirements in the Act if it can be shown that the betting is a non-commercial activity. For example, no licence is required when a company's employees all enter a Grand National sweepstake etc. Likewise, there is nothing to stop me having a bet with a couple of mates in the pub that my footie team will beat another.
My gut feel is that, provided the proposed betting scheme is relatively small scale (less than a 100 punters for example) then it shouldn't fall foul of the Act. If its run on a sweepstake style basis then that should be fine. Its trickier if the individual is offering odds and taking bets (for example, how is he going to finance his losses?).
I strongly recommend that the individual who wants to set up the scheme sets out his proposals as clearly as possible and gets them approved by a solicitor who knows his stuff - I'm just not in a position to give you cast-iron advice on this.
Chalks.