This is no reflection on your parenting skills, and don't know what they are like as people, but I would your 2 leave home. I have mates who stay at home and really regret not living in halls with other students. It also helps making friends as you live with/next to people for a whole year and...
You can get 2 loans from the goverment. The £9,000 one which goes straight to the university for fees, then, depending on household income and other factors, around £4,000 a year which covers accommodation, food, books, night out.... My mum doesn't help me and I have managed so they should be...