Privacy has been difficult (if not impossible) for the average individual to maintain since the Anti Terrorism, Crime and Security act of 2001 (later replaced by the Prevention of Terrorism Act). There are several provisions on both which could breach articles of the Human Rights Act... Anyway not to get political, but if the police or security forces want to find out information about anybody, they can. The question is are they going to bother gathering that information on people who are working within the law, paying tax, and don't flag any kind of "threat" radar.
My belief is that unless you are a native of a country which is high on the threat list, or you have ever belonged to certain political groups, or taken part in an anti-government protest, they are not going to be bothered.