Is it possible for a UK citizen to easily renew a 60-day tourist visa while living in Thailand for a year?

Come live in Chiang Mai. Plenty of options available. PM for details.

Bear in mind that working in Thailand without a work permit is illegal so I'd keep that quiet

Are you referencing the SMART visa, or the LTR Visa? If you haven't looked at the LTR Visa, take a look at that.

But to answer your last question, no. You can extend a 60 day tourist visa ONE time for 30 days, giving you 90 days total.

You can then leave Thailand and apply for another tourist visa at a nearby consulate, and then repeat for another 90 days. But after that you will probably start running into problems of consulates refusing to approve you for another visa, or border agents asking you why you are living in Thailand on tourist visas, which is not allowed.

You can try getting a multi-entry tourist visa while you are in the UK, which will give you about 9 months in Thailand.

This visa is valid for 6 months, and gives you 60 days entry each time you enter Thailand. You can extend for 30 more days. So 60+30, exit and re-enter 60+30, then just before the visa expires, you do one final exit and re-entry for 60+30, which is very close to 9 months total.