3: no ID check to disable a SIM?

Last week I ordered an iPhone 5. It uses a nano-SIM rather than the micro-SIM the 4S does so, on the advice of 3’s customer service people:

I went into a 3 shop to get one.

My date of birth and postcode were taken and I was handed a new nano-SIM. The packet includes a URL to have the SIM activated (with the proviso that when the new one is activated, the old one will stop working) but since I wouldn’t get the new phone till (at least) Friday, there shouldn’t be any rush to activate it…

This morning, my phone was showing “No Service” and switching it on and off again didn’t fix it. When I got to the office, I tried logging into 3’s attempt at a portal but my login was rejected because I apparently had the wrong SIM number.
When I got home tonight I put the nano-SIM (in the included micro-SIM adapter) into my 4S and lo and behold it works, with my old number.

So it seems that 3 cancelled my old SIM and activated a new one, identifying me only by my date of birth and postcode. It shouldn’t be hard to see how that neither uniquely identifies me nor does knowing those two pieces of information prove that I am who I say I am!