I think the TCAS spec is something along the lines of:
Prediction of less than 40secs and within 1200ft = traffic advisory
Prediction of less than 25secs and within 400ft = resolution advisory
Given that a 'high energy' aircraft could have RoC and RoD of 10000ft/min it is easy to see why aircraft flying in the proximity could have a TCAS alert even though separation is well in excess of normal VFR rules. In controlled airspace PMA 32dd is correct about the 500-1500ft RoC or RoD to prevent everyone in the hold at LHR taking avoiding action against each other. Of course the system only goes on data output and relies on accurate transmission of Mode C - if there is no altitude readout then only a TA is given. I think there was an incident (if not accident) in the far East where one aircaft was outputting an erroneous height reading and the other actually took avoiding action into its path!
I would imagine that civvies that take shortcuts to Aberdeen and Norwich etc will have a few of these TAs even though the 'offending aircraft' adheres to normal VFR avoidance rules - perhaps they just select RA mode and use the TCAS as a poor man's radar to get visual. A few spilt G&Ts over the North Sea would make top tabloid headlines and would probably result in airlines being mandated to remain within the airway structure - or perhaps encourage the CAA to establish some new airways!