I have never really got involved in this tbh. DD gets the basic maintenance loan and we pay her rent and that is it. The same plan is about to go into place for DS1. DD always seems to have plenty of money and reckons the only reason students run out is because they drink so much (she is a non drinker). She runs a car as well and we do pay the insurance on that as we have a multi car policy, but she pays for her own fuel (she doesn't drive to lectures, only to shops and when she goes out into the countryside or to the coast with friends). She does a sport which is not expensive and is in a society which is, but we do not pay for either. In the scenario you describe I would not be offering any more money to be honest.
We left DD to budget for herself and will do the same with DS1 - they are both pretty mature and have also both had jobs so know what money is worth. We have said we will be there to catch them once, but so far it hasn't been needed. I suppose if one had a very young and inexperienced person going straight from school who was used to having everything laid on you might have to take a different approach, but I don't get the impression that is what your DD is like DG.

This is really helpful, thank you.