Dan with all due respect you would do well to read some of the content re medical reports on this forum.
No marker or encoder can be added centrally, your registered GP is your data controller under GDPR and their are strict rules on who can access your medical records even for direct medical care purposes, and firearms are certainly not direct medical care. Your medical records are held only at your GP surgery their is no national central database.
These records depending on your age will be in two formats; Lloyd George paper records and for (most) us oldies together with digital Summary Care Records.
It is virtually impossible for medicert or any alternative GP to gain access to your paper records. They can, like you can, with your consent access your online summary care records. But unless you are a teenager theses will not be your medical history for your life. For example my SCR are for only 1/3 of my life 2/3 are paper records.
Yet the Kent and others police template letter ask your GP if you have EVER had or suffered from certain relevant medical conditions clearly unless you are a teenager medicert or the alternative GP cannot fulfil the EVER condition.
I emailed medicert several weeks back and asked them to explain how they were complying with the EVER condition but they have never replied.
To make a false declaration to obtain firearms by either the applicant or the GP is a criminal act.
However it is not the responsibility of medicert or the alternative GP to add the marker that you own firearms to your medical records this is done at the request of the police by your registered GP after the police have granted the certificate.
HOG2016. However if your GP has refused to engage in the process then it is likely they will not place the marker on your records.
And as my own recent experience of renewing my own certificate has shown when I stated to the FEO he did not need a GP report because I have a marker in my medical records he said the report was still required as even with the marker GPs have no legal duty to inform the police if you start to suffer from any of the relevant medical conditions.
So a one day in five year MOT.
This is a mess. But we have to keep paying and playing the game.