In the UK (my home country - though I am currently living in the US) there is no compulsory requirement to carry ID at all times and unless a police officer has reasonable cause to arrest you, a citizen (sorry, 'subject' of the crown ;-)) is under no obligation to identify himself or herself to a police officer. There are of course some exceptions to this: for example, noone may lawfully drive without a photo ID driver's license and a traffic cop can require you to present it if pulled over.
Since the introduction of more intrusive anti-terrorism legislation in the UK, police are able to conduct 'stop and search' in certain designated areas (likely terrorist targets, stations etc) entirely at random. Normally, police have to have reasonable grounds to stop and search.
I have been randomly stopped and searched on such basis once at a major London railway station. When the junior police officer conducting the search had finished rifling through my camera bag, he asked for my personal information - name/address etc. to record in his log book. I politely told him to get stuffed unless he had reasonable grounds to suspect that I had committed or was about to commit a criminal offence, in which case he could arrest me. Furthermore, I asked junior plod to identify himself to me by his badge number and station and I diligently recorded the details in my notebook. He was quite ruffled by all this and went to speak to his sergeant. I'm pleased to say that the sergeant confirmed that I did not have to personally identify myself to junior plod, who instead took down a physical description of me in his book.
Cling to your liberties. All this compulsory identification is largely useless as far as I can tell. They're quite obsessed with it in Spain (where I was living and working in 2007) but it didn't seem to thwart to atrocities that took place there in '04.