ZARP doesn't need to be registered as a company as there are profit requirements before registering as a company is required, and nobody is employed at ZARP - all staff, including the Community Team, are unpaid. I am unsure if the profits made by ZARP are enough for Chute to be registered as self-employed, however they are not enough for any taxes to need to be paid.
There is no register of Copyright in the UK, and you do not need to "apply" or "register" for it - anything you make is automatically copyrighted, that is the entire concept of Copyright:
www.gov.uk/copyright