Let's get the terminology correct right from the start. You didn't come in on a '30 days visa' because there is no such thing. You are British so you came in on a 30 day visa *exemption*. See chart.
It's called an exemption for a reason. Citizens of numerous countries are eligible for that if their stay is for 30 days or less. It's to negate people having to apply for a full 60 day tourist visa from a consulate or embassy outside Thailand.
Looks like you'll need to go back to the UK to apply, depending on what visa you want. When you get back, call the Hull consulate, who are the most helpful and friendly of all.
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