The cam belt is a serviceable item and is considered 'wear and tear' under most warranty policies. Therefore, if the belt failed, it most likely would not be covered by the warranty.

You do have legal rights, the 2015 Consumer Rights Act allows you to claim against the dealer if the belt failed within the first six months. But I would not recommend buying an eight-year-old car that's still running on its original belt.

Tell the dealer you want the cam belt change to be included in the deal or you will find another car for sale.