I think maybe an accountancy package might be the way to go but the ones I looked at seemed to be too 'businessy' if that makes any sense? Just too complicated for a very small business..
I'd definitely give Free Agent a look then. It uses deliberately everyday language. For example, 'creditors' are called 'bills', which is nice and easy to understand. It will integrate with most online business bank accounts, and pull in transactions automatically. Then, say you'd raised an invoice for £120, and a payment of £120 comes in, you just have to confirm it's 'guess' that the two transactions are related. No double entry, no balancing books and no messing about.
There's also a month's free trial, so you can give it a go without risk.
P.S. Many smallholdings do register for VAT, despite being under the threshold. That's because food products are zero rated whilst things like buckets and vet bills do attract VAT. The upshot of that is that your customers don't have to pay any more for their meat, but you get to reduce your running costs by reclaiming your 'input' VAT (this is all automated within FA in our case, so doesn't take any time at all to do). Your own case might be different if you're selling teaching services or other goods, but it's worth doing some projections to see what makes most sense for you.