No.
If nothing else, to be able to get medical treatment on the NHS, you need a number - not having one into adulthood (which is what deleting it would cause) would flag up possible identity theft, illegal immigration, terrorism, etc. If somebody is also of non UK origin/ancestry, it could also put them at risk of being deported, as they wouldn't be able to prove they had been in the UK.
IF you are wondering in the case of an abuse situation where the abuser might be able to access medical records as part of their job, that's different, as contacting the HR of their Trust should be able to ensure their computer use is carefully monitored (accessing records you aren't required to open as a direct consequence of your job is a sackable offence).
IF you are being threatened that you will be found wherever you go, get advice from Women's Aid.
And IF you have been told by somebody their record was deleted, assuming it isn't where multiple records were opened and then merged under one number (they're crosslinked on the computer systems), if it's a personal relationship, be careful.
And IF you're an NHS worker and thinking of going a bit Miss Marple on somebody, no good will come of this. If it's a 'so open me up a new file', refer to your manager. If it's 'I wonder if this is somebody that is on Witness Protection/is a person the Press would like to stoke rage up about?', keep the fuck out of it. It's not your job to nose around and you will lose your job if the information is released.