Is it legal for a chef to work unpaid hours?

Under the National Minimum Wage Act http://www.legislation.gov.uk/ukpga/1998/39/section/9 an employer must keep records of the hours worked. Working longer hours than is nominally contracted for could be an issue if this means that his pay drops below minimum wage for the hours worked or if proper records aren't being kept. The other issue is whether his working patterns are compatible with the Working Time Regulations. You can read about the Working Time Regulations here http://snipurl.com/28qak4k

only if it takes him below minimum wage. The ACAS website will be the best place to search.

If he is being paid salary then yes that is perfectly legal, that is one of the downsides of having a salary job. The benefit is that there are times he is not working or it is very slow, and he is still getting paid the same rate. It would only be illegal if he was being paid on an hourly basis and the restaurant wasn't paying him for actual time worked. I will point out that its very rare for a regular restaurant employee to have a salary. Almost always they are hourly, unless they are management.

Yes it is legal. When he began work he would of agreed to a contract, he will be led by whatever that contract says. My personal opinion does not matter, its what the contract states clearly that decides.