Yes, Nominet, the official registrar for .uk domains, allows this facility for individuals. Unfortunately, other domain registrars do not. So if you have a .com, .net or whatever, your details are always visible on whois searches.
Companies such as
http://domainsbyproxy.com/ allow you to withhold your details from whois searches. I run a webforum with a .com name and in the past I've even had to get a restraining order out on a member I banned (it's a mental health forum). A private registration ensures my privacy and safety - something I value highly.