Hi T's Mam - when a child is legally adopted, they should be issued with a new NHS number and a completely new record begins from scratch. Their old medical records should be closed down, and there should be no link between the old records and the new ones. Unfortunately, as adoption is a relatively rare thing, it's not unusual for GP surgeries to not be aware of the procedure. What can happen is that when you inform the GP of the adoption and the change of name, they just change the name on the child's original record, meaning that both the old and new names are on there and possible identifying information from their time with birth family is also on the same record so anyone searching the database can see everything, which is far from ideal.
In the old days, pre-digitalisation, what should have happened is that a new NHS no. is generated, and new file is created, and someone, usually a senior HV, will create a written summary of essential information from the child's original notes (vaccination, known health issues, etc.) to be appended to the new file. This document explains the process, and if you're having problems, it might be worth printing off a copy and taking it to your GP, asking if the procedure has been properly followed: https://pcse.england.nhs.uk/media/1247/adoption-medical-records-practice-guide.pdf
Here is a link to some guidance local to Nottinghamshire that details the challenges around digital record keeping, and the processes they have adopted there to ensure this is done properly. https://www.mansfieldandashfieldccg.nhs.uk/media/1941/adoption-managing-child-health-records-for-children-who-have-been-adopted-in-nottinghamshire-county-april-2013.pdf
So, the HV in your case is not correct that records have to follow the child. In the case of adoption, original records absolutely do not follow the child, and it is the responsibility of health professionals to ensure that key information is carried over, but identifying information is redacted so that anyone looking at the new files would not see any reference that could identify birth family by name, location or other identifying feature. This can cause problems where children (like mine) have extensive medical histories before adoption that need to be retained, but it is to preserve anonymity for the adopted person.
This issue comes up so often that it's a wonder that prospective adopters are not more thoroughly prepared during assessment and training - it seems that very few adopters are given proper information about this, perhaps because social workers just assume that the NHS will do its job, but as I, and many others, have found, some prompting is sometimes needed!
Just as an aside for anyone reading this, if you adopted a child in England who had already begun compulsory education and been issued with a unique pupil number, the same process should happen: their old file should be closed, a new unique number created, and a new file created. Again, unaware of the procedures, some schools simply change the child's name on the original file. This can mean that, depending on the settings on their digital files, documents can continue to be automatically generated with the child's birth name printed on them. Parents adopting school age children should consider going down to school and making sure this procedure is being carried out properly.