At my workplace (Textile Business that controls yarn storage, operational Looms etc) we have numerous heavy duty Fire Doors separating departments. 

I noticed many months, almost half a year ago, that some of these doors didn't close properly even when forced. I instantly reported this to the Health and Safety team as is expected of me. This was 5 months ago and still no-one has acknowledged my query or done anything about the doors regardless of my constant reminders. 

As you may imagine I've simply had enough of their ignorance to our safety and wondered if anyone on here would be able to help me find a way to get through to them? Also how liable are they for this?

Possible breach of article 13 of the Fire Safety Order (relating to escape routes including their protection by fire doors) which is a criminal offence. The employer would be liable, plus any staff with control over an issue could be liable as well depending on the circumstances.

If you are getting nowhere then the fire service would be your next port of call assuming you don't have a union to involve first.