I have just discovered what was wrong. The “Remote Recording” setting in Advanced settings in the box was set to Off. Now I have put it On, the app on the iPhone seems to be generally working.
It shows all the schedules from the box and the box receives new schedules from the app, There is a bit of a delay in transferring things, but that is down to the Update Interval which has a minimum setting of 10 minutes.
It seems to be a bit confused over semi-expired schedules which get listed at the bottom of the list on the box (“Getting information fo…”). It shows some and not others.
Edit: I have just noticed that the app does not seem to be able to delete a schedule once it has been set up.