Check your tenancy agreement. Usually temporary absence from the property during term time won’t change your situation. Especially for Cambridge where terms are so short and many colleges don’t allow you to stay over holidays. Even better speak to the housing team at the council and explain that you’re applying to university and get confirmation from them in writing that it’s not a problem.
As a student you would be exempt from council tax too which means that your mum will still be eligible for single person discount on council tax for the flat.