How can I extend my 60-day stay in Thailand from the UK and what are the requirements?

The extension is normally issued the same day. It can sometimes take some time, and when the first stge of handing in the form, with copies and money is just for lunch break, you might have to come back after lunch, to give you an impression about the process, but this can be different at different immigration offices. My experiences were at Hat Yai.

Krabi is a very friendly immigration office

Within the last two or three weeks is fine. They do it on the spot.

You need some passport photos, your passport and ฿1900 in cash. There is a form to fill in which you can get when you visit the immigration office.

VOA 🤦. No you're not. You'll arrive 60 days exempt of a visa. No visa.

You mean visa exempt?

There's no such thing as a 60 day visa on arrival. Visa on arrival is for a small group of countries who must apply for and pay for a visa at the airport.

If you have a UK passport then you qualify for visa exempt (not any visa. It means you are exempt from needing a visa) and will receive 60 days permission to stay. You can apply one time for a 30 day extension. Most immigration offices will accept an application for extension when you have 30 days or less left on your entry stamp. You'll receive the extension immediately when you apply, you don't have to go back for it.

Attached is a list of common requirements, but each immigration office sets their own requirements so it may not be the same.