With regard to the problem on your Xperia Z3 Compact, are you sure that its operating system is up to date? Your phone was sold with Android 4.4.4 on it. The NHS app requires Android 5.0 or better so, in its 'out of the box' state your phone can't run it. However your phone is upgradeable to Android 6.0, which should then allow the app to run.
So, if you've not checked that the phone's operating system is up to date, that's clearly the first thing to do. If it is, and the app still won't work, try uninstalling and then reinstalling it.