By passing an RFID chip over a card reader you are also passing it over a small induction loop that temporarily gives the small charge required for the transmission of the information. There are no batteries involved so there is no capability for continuous or intermittent transmission as speculated.
Didn't someone do a demonstration in the USA recently where they drove around managed to interrogate a significant number of RFIDs in US passports(?).
Passport RFIDs cloned wholesale by $250 eBay auction spree
I think what worried people in the UK is that the government (and particularly the present one) have a terrible record with any sort of computer / IT project with them going way overbudget, being late and insecure.
They initially talked about a completely voluntary ID card system at low cost then started to introduce by stealth in different areas, the cost has increased with talk of £1000 fine for not notifying of any changes - a new card has to be issued after a marriage name change and paid for. It is obvious that we will be eventually required to carry them all the time eventually if the government gets its way.
There has been a lot of spin about them so it is hard to get the complete true story - I get the impression that most non-police users will possibly not be accessing the full details on the card so it is just another piece of plastic with name and photograph. Even the average police office on patrol might not be able to access it.
We have the Home Secretary going around saying that there is overwhelming public support for them but every independent survey has shown the complete opposite and most opposed to them.