I can confirm all that you say above regarding the NHS app, Warwick, although I'm not sure that a minor tweak will be sufficient to present vaccine information in an easily readable form for -- for example -- Greek immigration staff. The app is user-friendly enough, with a short menu on the home page. In the section "GP Health Record" there's a sub-section "Consultations and Events" which includes evidence of vaccinations, with the date, location, vaccine type, batch number and name of the person administering the jab. But as it's a timeline, any other consultations or events, such as test results or GP appointments, are listed between the two vaccine dates which are three months apart. Therefore, in order to show this information at departure/immigration you would first need to log on to your NHS app then navigate to the list, then spool up and down to identify the two vaccine events -- all with a long queue of passengers behind you! It's not really a viable option in that form. A QR code would be much better and I can't see how the app could be adapted to provide one, but perhaps someone is working on it.