Can I enter Thailand from the UK without a visa, extend my stay, and travel unvaccinated?

If you arrive without a visa you'll be stamped in for 30 days visa exempt and you can apply one time for a 30 day extension.

There's no requirement to be out of the country any amount of time to be able to enter again, you just need to actually enter another country by passing their passport control before returning to Thailand.

If you need more time there's really no reason not to apply for a tourist e-visa before you come. With a tourist visa you'll be stamped in for 60 days and you can apply one time for a 30 day extension.

The evisa application fee is cheaper than the extension from immigration and from London it takes about 3 days after your submit your application to receive it.

You're limited to entering Thailand 2 times at a land border without a visa per calendar year. But there's no limit written in law for entries by air. That being said you also cannot enter an unlimited amount of times as you'll eventually be pulled aside and asked why you're spending so much time in Thailand on short term visas.

Yes get 30 days. Then the easiest way go to an agent to extend for another. Saves you filling all the forms in. The border runs are a nightmare. This agent is excellent at getting extensions fast.

Yes, you will get 30 days visa exemption on arrival, which may be extended by 30 days at the Immigration without leaving Thailand. After that, you can do border runs 2 times in a calendar year by land borders and repeat the process. And at least in theory unlimited number of times by air. On a border run, you do not have to stay in the new country for more than 10 minutes, but you need to stamp into the new country, i.e. you will need a visa for that country.