A lot of insurance policies cover students living away from home but you should get your parents to check with their insurance company to be on the safe side.
I agree with saffstar the level of cover can vary - I was supposedly covered under my parents insurance but when I lost everything in a theft/arson attack I found I was still massively out of pocket due to exclusions and out of pocket expenses which would have been covered if I had a seperate policy. They don't cost much for the peace of mind - I would recommend Endsleigh Insurance who used to specialise in student insurance (if they still exist). Good luck in your studies.
Endsleigh were crap when dealing with a few friends of mine claims! For example "shared house" insurance against theft is almost impossible unless every student in the house is insured with them.
Even then the % they offer aint worth it. If you got anything valuable, leave it at your parents that what I say.
The most affordable contents insurance for students is provided by Saxon Ins. Endsleigh are a joke considering it was originally set up by students for students.