You can get a licence on a simple visa exempt entry. The fine isn't 50,000 baht yet. It's a proposal for a law change and will take at least a year to become law.
If you attempt that here in Thailand, you WILL need a police report. You'll also be without a passport for around 6 weeks or more. The UK don't just send another out on demand.
Elisa Cohen then i think that could be the mystery solved as to why your visa has been marked 3 entries. I'm guessing its highlighting the fact your living here or at least, spending too much time here on tourist visas and has highlighted the number you have previously.