I suspect the problem is that I returned the old iPhone 6 to the Apple Store as it had a frozen screen. The store couldn't get it to work and replaced it. I therefore no longer have the device.
In iTunes (third point above) I can only deauthorise all the devices, not just the old iPhone 6.
In iCloud (first point above) I have removed the old iPhone 6
In the Find My iPhone app (second point above) the old iPhone 6 isn't listed, just a generic "iPhone" which is offline.
The red badge with number 1 is still there on the Settings icon on the phone.
There must be a proper solution to this problem, which seems to have been caused by me installing 10.3