Can I apply for a retirement visa in Thailand after arriving with a tourist visa?

I would suggest applying for a tourist visa, which will give you 60 days and you extend it for another 30 days. This will give you an initial 90 days instead of 75 days.

Here is another option for you, and gives you absolutely no worries about getting an extension a few times, or leaving the country on a border bounce, and wasting precious vacation days. From your comments I assume you have the equivalent to bt800,000 in your bank account in the UK. And you have no qualms about getting insurance (travel insurance doesn't work), because it is smart to have anyway. With these two things, and maybe a police clearance, you can apply for a type O-A visa based on retirement at the Thai Embassy in the UK, and get a multi-entry visa good for 1 year in Thailand. Then when it gets close to the end of that year, you leave and come back in, or if you are out of the country anyway, you just enter Thailand, and get another year, but on this second year when you leave it becomes voided because you've passed the original year. After you get this O-A retirement visa from the Thai Embassy it is good for 6 months until you enter Thailand. If you don't enter the first time within 6 months then it becomes void. Timing everything right, you can get almost two full years out of this multi-entry visa. An important thing to remember though, is you will only be stamped in for however long your insurance is good for. This covers many different vacation options for you over about 13 months, before you can't enter on it anymore, but you can stay up to a year on your last entry. And, you don't have to extend it here, or border bounce. Everyday is pure vacation time.

No insurance requirement for a Non O based on retirement but to be honest I think you’re better off going with the second option of 45+30, then a border bounce to repeat. You don’t have to stay out of Thailand any set amount of time. Just cross to another country. Stamp in and out of there and return.