I don't really see why I couldn't give myself a sound understanding of the syllabus by reading up on it and using past exam papers.
No doubt, but it isn't whether you believe you could do it well or not, it is about you 'selling' what you have to the customers.
Two adverts : One is a current, or recently retired A-level English teacher, and the other is someone 'who has an English degree so thinks they might be able to tutor people' - which would you pick for your dc if looking for someone to tutor them to a better grade ?
I'm not saying you would never find anyone, and, gradually, over years, build up a reputation if you are good, but you have asked if it is a realistic full time career.
Would it be possible for you to try doing some alongside your current job, and both see how much you enjoy it, and what you can realistically earn from it before deciding to go full time ? Potentially, building up a local reputation if you are great at it, at the same time ?