Unfortunately, now that so much can be done via online/phone apps, an awful lot of sole traders etc are doing their "books" themselves supported by their accountant, especially with automatic bank feeds, online invoicing, online credit card payment, etc. There really is very little need for the "traditional" book-keeper anymore for the smallest of businesses.
Bigger businesses usually have their own in house book-keeper/admin.
So, your "market" is really either sole traders who can't be bothered to do it themselves, or that "gap" between the sole traders and larger small businesses, i.e. those with maybe 2/3 employees where the owner maybe too busy to do it themselves, but, for those, they'd probably want someone to do their payroll too.
Rather than basic book-keeping/admin, I'd say the real market is payroll, VAT and CIS returns, which is where things get complicated and a small business owner can't really do them themselves as they don't have the time/inclination to learn the rules, procedures, etc.
So, if anything, I'd suggest you set up as a freelancer doing payroll, VAT and CIS, but obviously, you'd need experience and knowledge to provide those services, and preferably a payroll/book-keeping qualification.