Ian - you have been given advice upthread about how to break your way in to this and book a vaccination but I thought I'd look to see "how rare you are" ie how many people in UK are not registered with a GP (and therefore haven't got a current NHS number).
The
NHS Digital site offers an insight.
Reducing this to England (total population of Northern Ireland, Scotland and Wales is about 11M)
60,744,002 patients registered at GP practices in England as at 1 April 2021.
The population of England (2019) is about 56M.
So there must be duplicates or NHS Digital is still counting people who've emigrated or died (latter about 600k a year).
Of interest, 93,262 registered in March.
@IanSmithCSE - You can be one of those who registers in April (though likely somewhere there is a number associated with you and your date of birth).
How many Ian Smiths can there be who are 60 this year? I'll leave our resident mathematician to work out the chances of two Ian Smiths aged 60 this year having the same birthday. There are about 393k males (Ian - assumed) any name who'll have their 60th birthday this year, god willing.