Yeah a Thai passport is not respected the world over. Many have ruined it for many others.
Just taking the mrs to Philippines was a ball ache at immigration and she was visa exempt. About 100 questions with frustrated people in the queue behind.
I don't even consider taking her to the UK. Why go through all that just to get rained on and taxed?
I'm not quite sure why you asked for advice. If this is very straightforward then any agent can help you. Thai Visa Express in Pattaya or Jo Rets i have used before. Both in Pattaya, both good.
You used to be able to do this. But you must now leave the country, or that is what I was told. I went to Philippines and in Makati I got my non b in 4 days.