Tim is at university, which was only for those who could afford it.
It wasn't. Only about 10% of teenagers got the requisite A levels and went on to university, and I would expect the majority of those came from better off families because their children were more likely to get into the grammar schools, private schools and the better comprehensive schools, and poor families needed the income their children could earn from 15 or 16, so they tended not to stay on for the sixth form.
However, if you did get the A levels and a university or polytechnic or teaching training college place, the LEA paid the fees. Students would barely be aware there were fees. Students were eligible for a grant (i.e. non-repayable) for their maintenance. If you were under 23, this was means tested against your parents' income, and if they had an above average household income you got a bit less because it was assumed they would and could make up the difference. Not all parents did, but most did, and anyone from a low income family would get a full grant.
Once over 23, you were a mature student and it was your own income that was means tested.