OP I sympathise. The uni years are difficult for middle earners. Looking back to when my children were small, the fact that contributions would be expected from parents for a university education, let alone the likely sums involved, were never publicised. This is still pretty much the case. You have to go looking for the information, which discriminates against families with no previous experience of higher education.
I feel that it is so wrong to means test any person aged over 18 by their parents’ income, it infantilises them. They are treated as an independent adult in every other respect so it is not surprising that you did not realise that your income would affect their education, the mantra has been ‘everyone can afford to go to university which isn’t true for children of unsupportive middle or high earning parents.
However we are stuck with the current system. We felt strongly that our children should receive the same amount to live on as those on a full loan and see it as our duty to make up the shortfall. They are expected to pay for everything out of this but get free board and lodging in the holidays. If they want a more extravagant lifestyle they work for it in the holidays. A gap year would also allow your DC to save a nest egg and probably be a great experience.
Assuming you feel it is right to do the same, in your situation I would look at a budgeting site e.g. money saving expert and go through all of your finances. It is amazing how much you can save by looking at where each £ goes, switching utilities, cancelling old subscriptions etc.
Check your tax re the car and fuel and look at more cost effective options, it sounds as though significant savings could be made there.
Encourage your DC to study a 3 year course. Some are 4, 5 or 6 years long!
A good education really is the greatest gift you can give your DC . It will be worth the sacrifices.