Can I get a retirement visa in Thailand after entering with a visa free entry?

Very possible but more running around, cost. My recent experience, I had to get thai license, immigration paperwork, purchase 1 years insurance to open bank account on tourist visa and apply for non o based on retirement. It's definitely easier to do if you apply from you home country then apply for 1 year extension once here.

I got a retirement visa before I came here. Always better to be prepared.

We.did that about 2 years ago but now it's hard to get the bank account which you need for the visa. Before we could buy medical or bike or life insurance from the bank which allowed us to open an account. That seems to have gone away .... Things change constantly

Getting the 90 day non-o before you travel would be sensible as it will make it easier to open a bank account, you'll need to have funds in the account for 2 months before applying for an extension

There is no "standard visa" that you get on arrival 😕

As a brit showing up here without having bought a visa from the consulate before you come here you'd get stamped in FREE entry (visa exempt) for 30 days (the 60 day visa exempt program has not started yet).

BUT

with that being said

Yes, you could indeed show up here free stamp entry, get 800K baht in a thai bank account in your name only and then apply for the 90 day non-O visa at the immigration office where you will stay in thailand.

OR

You can apply for the 90 day Non-O visa based on being over 50 (retirement) online at the thai consulate in London, show up here get stamped in for 90 days then apply for a year extension on that visa (you wouldn't convert it to anything you'd just apply for a year extension at the immigration office).