The level of traffic information passed is is dependent on the type of service. Most VFR traffic in class G airspace will be receiving a Flight Information Service (in UK airspace) - assuming of course that they are talking to someone!
The rules here permit radar identification of FIS traffic for the purpose of "monitoring and co-ordination purposes only". But we are also permitted to pass "information pertinent to safety", and most controllers interpret that as including some form of traffic information.
Personally, so as to leave no doubt in the pilot's mind that he IS NOT under a radar service, I only pass generic traffic info to FIS traffic (i.e. "traffic passing point X NE bound" as opposed to "traffic in your eleven o'clock"), and I don't identify anyone unless they are operating in an area likely to directly conflict with my IFR traffic.
Hope that's of some help.