Can I keep my insurance policy running if I sell my car?

I am looking to sell my car within the next couple of weeks as I am soon leaving for uni but my insurance policy doesnt run out until the end of the month. Having spoken to the company they have told me it would cost £120 to cancel the policy early despite only having a few weeks left on it. I need to sell the car before I leave as I need the money to fund my first few weeks of uni. Can i leave my current policy running until the end of the month and still sell the car, obviously the person who buys it will want to insure it straight away?