International pet travel is very complicated. There is no shortcut. You have to work through the export and import of both countries. I looked at traveling to South Africa with my dog to represent the USA at the dog agility World competition, and I was astounded at the amount of paperwork, shot records, titer tests and more that had to be conducted.
First check the UK's governmental websites to find information on what they require for dogs coming into the country. I would expect the UK to be pretty strict about these requirements. Be prepared for needing numerous vaccination and health records to be completed. There will need to be lab work done to test for various illnesses. You will need to look at the requirements for actual shipping, including airlines, cargo and those requirements.
You can hire a professional "pet carrier" to help you wade through the legal red tape. This is probably your best bet, as they will know the governmental requirements of both Thailand and the UK. For dogs staying to live in the UK, you may have to deal with quarantine.
You MUST go through the governmental agencies, and requirements to ship. There are no shortcuts. Remember, the UK is protecting their animals by making sure any animals from outside do not bring in a dangerous disease. These laws are important and necessary. Abiding by them is important and necessary. Plus, there's no other option. :)