"Don't we all have to go through certain checks to prove who we are, where we were born and if we have a NHS number and NI number etc, etc?"
Not the last time I went to hospital, AOG. I just pitched up and (after a fashion) they saw to me. Yes, I gave my details but I doubt very much that they were checked to ensure I was bona fide. In fact many in the sawbone profession have said they have no intention of making such checks as their job is to heal the sick (wherever they might hail from). It seems to have escaped them that they also have a duty to protect their employers (the taxpayer) from fraud, but there it is.
However, that's a State funded organisation. There is no reason why private suppliers should have to check the credentials of those wishing to use their services (with the threat of criminal sanctions if they refuse or fail). What next? Tesco's needing proof of entitlement to buy a pound (sorry, a kilo) of spuds?