"My cousin will be leaving uni in around £40k worth of debt with a good English degree, after just 4 hours of tutor a week."
IF she was only doing 4h of tuition a week, why in hell didn't she have a part time job at the same time, even if she was at university? They don't ban you from working, you know!
I had a Saturday job throughout my university years - plus working every holiday as well. I also did a 4y sandwich course with a year of industrial training (paid) as year 3.
I lived at home - my parents thought about charging me rent, but my grant (yes, I'm that old) was reduced to accommodate the fact that I lived at home, and so barely covered my train fare. If I hadn't been working as well, I'd have had to get my parents to subsidise my stationery requirements, let alone clothes, nights out (few as I didn't live near the rest of them and had to catch the train home) and lunch.
Back to the OP - I was working from the age of 15 in Saturday jobs, but my parents didn't ask me for rent. They wouldn't have. I offered them money from my first wages and they told me to put it into a savings account instead, which I did. If I'd frittered it all away, perhaps they might have taken some off me, but I suspect that they would have saved it for me. They weren't well off by any measure of means, but they weren't so poor that they needed rent from me.
So YANBU - unless they absolutely need the money to pay for food to put on the table, then no, I don't think it's reasonable to charge your A-level student rent.