JollySanta, you've completely missed the point about addresses, etc.
First, you need a huge IT system and many people to administer this (constantly changing) data. You have to pay for this.
Second, it becomes a law against honest people, who spend their lives diligently trying to submit Form X and Signature Y and Document Z (and forgetting or losing stuff, as you did). While those trying to get round the system will lie about address, borrow or steal other people's cards, pretend to have had their handbag stolen, etc.
If you say no treatment without a card, you deny treatment to entitled citizens who really have had their handbag stolen or their house burn down, or have forgotten to post something like yourself.
If staff use their discretion, this makes medics immigration officials. You don't need a crystal ball to see that "discretion" will act differently on white people with an apparently British accent than for, say, brown people with a Pakistani accent.
And so on.
Every single way of trying to police this is difficult, resource-consuming, expensive and prone to error, appeals and legal costs, and to injustice and serious harm.
And for what? To not give healthcare to people who then end up in A&E anyway with preventable complications.
We have not spent the last 60 years "papering over the cracks" by declining to go this route. We made an active decision to spend the money on providing healthcare, not depriving people of it.