If you are finding it hard to get the figures to add up, it is worth asking about bursaries. Some, UCL and Imperial are examples, but many Universities offer something.
By 18 most parents know what their DC are like. DD was never particularly interested in money, and had friends who were similar. This is despite being at a school with a number of fabulously rich families. Indeed seeing some try to prove their worth by flashing the cash, like having not one, but two new iPhones on the morning of their release, was an effective inoculation. You can't buy friends or respect.
Ditto at University. The girl with the brand new BMW, a reward for having achieved her place is almost starting with a handicap when it comes to making friends (unless she plays sport and others need lifts). DD had quite long terms so all in all she spent about £75 per week and her friends, similar. Her University has a reputation for attracting better off student from the South East, and if DD had wanted to hang out with them she would have needed more. Instead her group, largely from Wales, Ulster and the north, and mainly from state schools, are quite outdoorsy, so surfing, hiking, wild swimming, and camping, rather than clubbing.
DC who like buying new clothes, spend a lot of toiletries, or like sitting in bars and cafes, rather than having friends round and cooking for them, will spend more. Parents should not feel obliged to fund a student lifestyle that they themselves cannot afford.