What is the legal situation regarding taking a home baked cake into a restaurant to surprise your friends?

I invited some friends for a meal at a restaurant in England. One of my friends had made a cake & surprised me with it at the end of the meal. I asked the restaurant if they could cut it up for us to eat. The response was no, the reason given was because of health & safety. Are they correct? If so, where can I find this regulation, can't see anything on the HSE website.