You need

First : Rabies shots

Then : Export permit + most likely a bloodsample to prove the rabies shot

And : Airline that will allow dog to fly + a cage that matches the airline guidelines

And of course : you need to read up on UK import rules, quarantine and stuff. 

You can find pet relocators. Be aware it is an industry rife with fraud, so do your research. There are some of them that can do full relocation but some can also just do part of the relocations such as all the paperwork in China. 

You are going to have trouble...my friends took a dog to OZ from Korea. Island nations have much stricter regulations on this topic. I recommend talking to somebody who has done it...try a pet forum.