Can I renew my UK passport while in Thailand and how does it affect my visa status?

Which passport are you discussing? I presume it is either British or Thai, but it could be something else.

If you hold a British passport then of course you can renew it in the UK.

The one day Premium Service is great in London. Apply in the morning and get your new passport later same day around 5 ISH. Bit pricey but worth it I think if you want to get your passport sorted ASAP.

If you change passport then you need to show both when returning, your passport is probably cheaper in UK then Thailand (I’m from Sweden and it cost 5400 baht to renew).

Visas are personal so you can move it over when returning, you can actually ask immigration officer to do it for you.

No problem, just get a re-entry permit before you leave (or at the airport while in the process of leaving) then use both passports to re-enter and afterwards go to Immigration to get your relevant stamp(s) transferred

Sorry this is such a naive post. Why on earth do you need to visit immigration to tell them you are going to the UK, why do they care what you do. You don't say what your permission to stay in Thailand is, I assume a Retirement extension. If this is correct you need to get a re entry permit at immigration or at the airport on departure, otherwise your extension will cease and you will have to start again. You also don't say how long you are going to the UK. Assuming it's long enough I suggest you renew your passport in the UK, why on earth would you wait and do it in Thailand. Remember you would need 6 months validity on your passport to travel to Thailand. Once you have your new passport, you simply present both to the immigration officer on arrival in Thailand. Once in Thailand visit immigration at some point to have any visa stamps transferred to your new passport. Rather simple and common sense really.

Renew your British Passport inside the UK as it much simpler to renew and many more options available to British Citizens for renewal, such as submitting a renewal application online inside the UK, and faster options are available inside the UK to get your British Passport processed very quickly, such as 1 Week Fast Track and 1 Day Premium

As long as you have a re-entry permit before you leave, you can return to thailand with both your old and new passport. They put the entry stamp into your new passport since the old one is invalid. Then you would need to go to immigration to get the extension moved over.