When we registered with our GP, we had to fill in a form stating whether we wished to go on the donor register. We ticked yes, of course. I thought that was a great idea as although we WERE on it anyway, I probably would not have remembered to notify them of a change of region. In fact, I think I was on it under my maiden name!
There are loads of ways a mailing can take place if the Government really wanted to- a form with CTC forms / benefits / pensions / IR forms; with Dr registrations; DVLA notifications. Most people would be hit by one of these at least.