You're a UK resident, so you can enter on a visa exemption, which since Oct. 1, will give you 45 days, with the possibility to extend for another 30 days inside the country. That will give you 75 days. You can leave the country and re-enter to get a new stamp. If you need 83 days, getting the Single-Entry Tourist visa would be better, since that would give you 60 days, and possibility to extend for another 30 days inside the country, for 1,900เธฟ.
According to the Thai eVisa website, as a UK you can apply online.
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