Aside from the bank details
Address date of birth and NI is all recorded any way isn't it, so it could have been accessed if someone wished to do so. I mean addresses were held on paper census in the public library. Its not that this was the only record of this information, just that it was all held together.
Re ID cards the cost does seem prohibitive. But aside from that, ID theft currently occurs as does other illegal scams. We live in a society where transaction/interactions are increasing global and not reliant on the fact the local post office knew your mum. I would have thought one system to verify ID was probably more secure than having to show passports which according to Fredrick Forsythe are easy to falsify and bits of utility bills - really secure.
On the whole I think the risks as well as the benefits of ID cards have been over exaggerated, so am fairly neutral to the idea.