to get a Non-Imm-O normally people have to apply for it on a Thai Embassy or consulate in their home country. yours is the UK, so your only choice is to apply for a 90 days Non-Imm-O Single Entry
in order to request for the "1-year extension of stay permit based on retirement" you need to change your visa status to a Non-O status, which will allow you to apply for said extension
do you have money 800K plus in a thai bank account? you can get a conversion from a 30 day visa exempt entry or a tourist visa, to a Non-Imm-O based on retirement, on your local immigration. SOME immigrations will be willing to do it . you have got to ask
are you over 50 years of age? Then the Non-Imm-O based on retirement would be a way, if you have got the financial proof. I see, that was your original question
and since the British Embassy does not issue income affidavits any more, you have to prove 12 months of incoming money from a foreign source by your Thai bank letter - "source" which can be whatever it is, according to the police order - which does not make any difference between income of state pensions or other income.
as long as you can proove the money, be it pensions or other income, comes from abroad to your Thai Bank account, the answer is yes. Only the bank book of ypur Thai bank account and their letter is accepted proof