How do I go about domain copyright infringement?

I have a registered domain name and copyrighted my company but I have been approached by a domain provider in a different country informing me that a company wants to register several domain names in different countries with the same name that I already have. They are being very pushy saying that if I don't respond within 7 days then they will accept the companies applications what scope do I have to make a copyright infringement claim and how do I go about it what are good sources BASED in UK