@Stuart ********
If you entered on a UK passport, you entered on a 30 day visa exempt, and not a 30 day visa waiver. You can get ONE 30 day extension of stay based on tourism at the local immigration office.
Different immigration offices have different policies, but almost all require the following:
1. Your passport and:
a. a copy of your data ("picture") page
b. a copy of your most recent visa (if you have one)
c. a copy of your most recent stamp
d. a copy of your departure card
2. A TM30, filed in the immigration office.
3. The forms (each immigration office may have different forms, and want to use their special forms)
4. 2x passport pictures
5. 1,900 THB.