Nominet might let them
Police are asking Nominet for the power to request a domain be blocked without a court order. The Serious and Organised Crime Agency (SOCA) has asked Nominet to move ahead with rules (PDF) that could allow law enforcement agencies to request a domain be shut down without a court order.
Apparently Nominet is OK with the idea. Currently Nominet’s rules don’t allow for domains to be shut down for criminal reasons, though in the past it has blocked domains at the request of law enforcement agencies on the pretext that they provided false contact details.
Nominet's plans will mean that suspension of a domain will not require a court order but should be limited to circumstances where necessary “to prevent serious and immediate consumer harm”. It would only cover serious crime cases in the UK which apparently means fraud, prostitution, money laundering, blackmail and copyright infringement. Not quite sure how prostitution and copyright infringement became a serious crime.
Nominet would only accept take-down requests from law enforcement bodies with which it has a trusted relationship so Neighbourhood Watch schemes are probably not included, nor local vigilantes.