I got my visa me type o married to a Thai in usa from e visa sight and it didn't seem to have an availability problem. That's just my experience from us not uk.
I came to Thailand on a ME type O married to a Thai I get 90 days. If you need more just re-enter and get another 90. Good for a years worth. At least you'll have time to apply for a different visa. It wasn't a lot to do to get. I did it through the thai e visa system in the US.
Check out USCIS website it lays all the forms needed. It is time consuming but they lay everything out for you. I brought my wife to America on a k1 visa and her daughter on a cr2 visa. Just takes time