My kids are early primary so I'm thinking way ahead (possibly unreasonable) but I would like to start saving for these costs now.
We did exactly what you are suggesting and put aside a small amount of money every month (basically, it was half of the child benefit) and put that into a cash ISA.
We weren't specifically thinking of university fees at the time just, as you said, something that they could use for whatever they want. With hindsight, I'm really glad that we did this. Fortunately, we were in a position that giving up some of the child benefit didn't put a strain on our income.
DD will be going into her second year of university in September and she's in London which is incredibly expensive. Our family income is such that she only qualifies for the lowest level of maintenance loan. If we were on the very lowest level of family income then she could get upto an extra £5k per year in maintenance loan.
She was in Halls in the first year and her maximum maintenance loan wouldn't even cover the full cost of the accommodation - never mind having to buy food, books etc.
Although, to be fair, there were other Halls that were cheaper but, even so, after paying the cost of accommodation, she would have have been left with only £450 for the whole year from her maximum maintenance loan and that Hall was miles away from the university.
So, we have committed to topping up her maximum loan to ensure that the accommodation is paid and that she has £75 a week to live on in term time (she had a job over Christmas but we gave her some money over Easter and she has a job arranged for the summer).
We chose £75 as that's roughly where JSA is. She's expected to pay for everything out of that, food, books, phone, clothes whatever.
If our family income was low enough that she qualified for the very highest rate of maintenance loan then that would cover her accommodation at the expensive Hall and £70 a week all year (or £90 a week just in term time).
If she went to the cheaper Hall then her maximum loan would cover the accommodation and £110 a week all year (or £140 a week just in term time).
Starting in September she's in a house share with some friends way up in north London and they've got a real long journey to get into the university on the Northern Line - but, hey, that's student life.
The rent they're paying for that isn't cheap either and her maximum grant just about covers the rent and utility bills and we're topping it up to ensure she gets £75 a week to live on.
Again, if she had qualified for the absolute maximum loan then that would pay the rent and give her £110 a week all year to live on.
But don't forget that living in London is stupidly expensive and things may be different elsewhere.