What documents do I need to apply for an extension of stay based on retirement (O Visa) in Phuket?

Seeing you still don't have a bank account in Thailand, you (as a UK passport holder) cannot apply for a visa/extension based on retirement until you have funds in Thailand. So, your scenario seems to be in the opposite direction.

What you need to do is this order unless you already have one bank account in Thailand

1. open a bank account in Thailand

2. transfer your funds

3. apply initial Non-O

4. apply 1-year extension

60days visa means you should have entered on a Single Entry Tourist visa. You can NOT apply for a 1-year extension based on retirement directly from the tourist entry stamp.

What you need to do first is: apply for in-country Non-O based on retirement when your current stamp still has MORE than 21 days (If my memory serves me right, Phuket has 21 days under-consideration period).

After 21 days of under consideration period (no stamp on a passport for this), go back to the immigration office to get a Non-O initial visa and admitted-until-stamp.

After that, you can apply for a 1-year extension based on retirement.

You need to get the latest handout for the initial Non-O visa from the Phuket office.

This is general information for in-country Non-O retirement visa application

/9.FOR-RETIREMENT-PURPOSES-50-YEARS-OLD-NON-O.pdf

You may need a Certificate of Residence from Immigration to open a bank account.

You can only apply for a conversion into a Non Immigrant O visa when you meet all the requirements. Get a Certificate of Residence and the hand out with requirements to apply for a conversion from the Phuket Immigration Office, open a bank account, deposit the money, get the bank letters and tick the list with other requirements before going back to Immigration.