Some brands do give long guarantees for their products but generally, for clothing which proves to be faulty, you can return for a refund for up to 30 days.
30 days to 6 months, the retailer should offer a repair or replacement. (I don't know if they still do, but M&S for example, used to have a 'zip replacement service' and I had a new zip put in jeans I had worn for several months.)
After 6 months, you only have those rights if the fault existed at the time of purchase. So, in your case, even a reputable High Street retailer could say it was normal wear and tear or similar.
However, any sort of warranty is only as good as your ability to enforce it. If the seller is ignoring you, then there is not a great deal you can do.
If the coat is worth it, maybe find somebody locally who will put a new zip in for you.
"There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.”
Søren Kierkegaard, Danish philosopher (1813 - 1855)
