Where to find solicitor in Belfast

I had accident in Northern Ireland, near Belfast, and I cannot find solicitor in England who could start with my case. They said it's dificult for them becuase Ulster has another legal system. Is it truth or may case is not good for them? And they don't want to tell me truth...

It was car accident - I was the driver, I was bit drunk, but it wasn't my fault. Men from Ireland hit me from back - he called polise and tell that I stoped so suddenly that he cannot stoped and hit me! It wasn't truth! Police also siad it was my fault, but witnesses said different. What to do now?