I did private tutoring via a large agency about 7 years ago and people paid £17-20 for GCSE and A-level - undergraduate level was higher. And travel costs were extra.
I'm not a teacher, and the agency didn't CRB me or ask for any proof of my qualifications at all, or even contact my referee! Actually none of the parents ever asked, either...
But there's clearly a desperate need for tutors - the agency kept calling me trying to persuade me I could get to all sorts of places by public transport. A friend is a full-time tutor (not a teacher, but has postgrad qualifications in the only subject she tutors) and charges around £22/hour. The tutees have to come to her, but she's near some large schools so it works well.
Finding exam requirements doesn't need you to be a qualified teacher either - they're often marked by totally unqualified people. My lab tech used to mark Science GCSEs and I ended up double-checking her as her English wasn't good enough and she'd not give credit if they used words she didn't understand.
I was a bit too honest and talked myself out of work, telling worried parents that their kid clearly understood everything they'd been taught so far, but to contact me if they had problems later. Probably why I ended up mainly teaching English to 14-year-old ESLers, rather than science A-levels.