What are my options for extending my stay in Thailand on a British passport after a 30-day visa exempt entry?

Fly out fly back in, now 45 days on arrival

let's clear up your terminology and get you dialed in if we can

You didn't get ANY 30 day visa on arrival as a brit because there's no such thing 😮

You showed up here without having bought a visa from a thai consulate before you came here and were stamped in on what's called a "visa exempt entry" (you get in FREE without a visa) and all you got was a free entry stamp <- not a visa on arrival, not a visa at all, just stamped IN free was all

You took the ONE 30 day extension you're allowed on that for 1900baht at the immigration office and you say that stamp runs out Oct 25th 😮

Unless you're married to a thai or have half thai children you have NO avenue for any extension after that one for 30 days you already got 😕

You need to exit/re-enter the country <- as in go to the border, stamp out of thailand, stamp in and out of another country and then back IN to thailand to get a new visa exempt entry stamp which will be for 45 days because they increased the time from 30 to 45 days now..

So depending on where you are in thailand you need to post on group related to that and see where people are border bouncing in your area and with who (as in what service people are using).

Leave the country an come back then you get another 30 days