Try not to worry. I went to uni as a formerly free school meals kid with £100 overdraft before I even turned up on my first day. Both my parents worked hard but you know what it's like, they were divorced and wages covered the bills and a few days out, not savings. Not a lot of people appreciate that's usually how life is, so you may get a variety of different views here.
It was an eye opener to see my housemates get their rent cheques from the parents and have money (especially when they claimed they were hard up) and I won't lie, at times it was tough, I put quite a lot on credit cards and worked 12 hour shifts in a factory over the summer. BUT going to uni was without a doubt the best thing I ever did. Moving to a new city, learning about the world, meeting different people and learning about a subject I really enjoyed. It inspired me for life and 15 years later I'm more than comfortably off, just paid off my loan and can now help my mum out. This would never have happened if I hadn't gone to uni.
It can be the best gift you can give a child, to be independent and manage their own way into adulthood. It's not easy but knowing that every penny I spent I'd have to earn back or pay off, gave me a decent ethic for these things. In contrast my DH is from a well off family where they could afford to pay for everything at uni, no loan and then be given money towards a house after, his younger siblings had more money given than him and are very unhappy and don't understand the concept of money at all because they don't understand the value of it.
I can save up for my kids for when they're older, but do I want to pay their bills when they go off to uni? Not really. I know the world is different now but don't necessarily believe the hype. Taking out a 12k loan in 2002 was chargeable high interest from day one and isn't written off for 45 years. That's a lot of interest and a long time. A larger loan today may seem daunting but is written off after 25 years (I think, or similar, certainly not 45) so in reality today's students won't be paying off much more, sometimes less, than we were back then (on median income.) Had I not paid my load off early, I'd have still had my loan at the same time as my own children, at least future generations won't have that.
Your children should be ambitious. If they want to stay close to home then great, but further afield there's a lot out there and it can be worth those extra shifts and a bit of struggle, they've got a long life ahead and education shouldn't just be for the well off, it's often wasted on them.