As of 26th May 2015, the use of exclusivity clauses in zero hours contracts is unlawful.
In March 2015, the Coalition Government enacted the Small Business, Enterprise and Employment Act 2015, which contains provisions on zero hours contracts.
The Act defines what a zero hours contract is, namely a contract to perform work or services provided by the employer with there being no certainty that any such work or services will be made available. The Act goes on to ban exclusivity clauses, which have the effect of stopping an employee working for anyone else, in said contracts. Therefore, any such restriction will be unenforceable against the employee.
The Act also allows for further regulations to be introduced in the future preventing further restrictions on those working under zero hours contracts. Prior to the election, there was talk of introducing anti-avoidance measures to deter employers from breaching the Act, for example fines, although there is no sign of these at this time.
If you have individuals engaged on zero hours contracts, it would be wise to review them so that individuals are not restricted in working for someone else, or if restrictions are present that you do not try to rely upon them.