Whilst they may be acting on behalf of the copyright holder this is nothing more than a simple begging letter. They can not instruct or demand that you pay anything, the only person who can do that is a judge upon issuing a court order.
They will never EVER take you to court, for exactly the same reason that companies who issue parking tickets never ever take anyone to court... because they can not demonstrate in a million years that the ACTUAL losses they have endured are proportionate to the amount of money they are asking for in their begging letter.
These are exactly the same as the companies/fraudsters who get a list of 20000 IP addresses and bang out letters to people who download films on PirateBay... ''Pay £500 and we will not take you to court''. Again, no one has EVER been taken to court.. they don't need to take anyone to court, they base their entire operating costs to make profit on 5% of the people just shitting themselves and just paying up straight away.... the 95% who throw the letter in the bin will never be contacted again.
Just finally, copyright infringement of this type would not be dealt with through a criminal prosecution, its a civil litigation matter... ideally just like parking tickets you shouldn't have replied and they would just move on... unfortunately they now know they have a 'live one'