I'm going to assume you are medically retired so would Muay Thai training be appropriate for you? It might be more appropriate to select a different soft power activity or even the Thai Privilege visa to see you through until you are 50?
Do you mean you've been working in Thailand without the appropriate visa to allow you to do so legally? Fortunately for you this is unlikely to interfere with a DTV application at a Thai consulate. Just remember you will need a letter from your employer confirming you are allowed to work remotely and that you will have no interaction with Thai entities or anyone located inside Thailand
You can get a DTV for medical treatment but you need a treatment plan for longer than 6 months signed off by a recognised doctor at the facility where you will get the treatment. That normally means you need to travel to Thailand for them to examine you and then come up with the treatment plan
You apply online wherever you apply but you need to be in the area served by the consulate you will use and remain there until the process completes. London doesn't require seasoned funds
Rather than appointment letters you need a treatment plan of at least 6 months duration signed off by a recognised doctor at the facility you will undergo treatment at