This is an issue. As far as I understand it (a parallel with quantum mechanics here- if you think you do.....) each GP- or maybe local health board or some such, has their own contract in to a private service that interfaces to the GP part of the NHS App, with a set of properties that someone decides (GP/company/board?).
Where I went to teach residents to us the NHS app a few months back, the patients can directly contact the GP service who hosted the session, in the app. Some of the residents were from other GPs, who couldn't contact theirs ( nor can I. The GP can send me a message- but I can't f****ing reply to it except by phoning them!!!).
They also send me texts I can't reply to btw!
"Please send us a blood pressure reading". Sure, Why not make it as difficult as possible to do so.