The indicated link sorted me - original source is iMore - Allyson Kazmucha. Method below. Another successful method I have since read is to backup your old phone to a Mac with iTunes and restore the new phone from this (rather than the cloud). Then re-download your purchased / free apps after this in the normal; way.
In my case it was an iOS 5 Cloud backup (from iPhone 3) to a new iPhone 6 which had shipped with iOS 8.1 (April 2015) UK. I could not update the OS (greyed out), could not backup and had the restore incomplete message (and a home screen message saying the restore process was ongoing). I gave it 24 hours plugged in next to the router (strong 4 aerial WiFi) - no change. *
Following advice on the site, I searched through the apps and found one stalled - I deleted this and then started the app download again (less than 60 seconds this time). I then did the hard re-boot (Power button and home button together 3 seconds until black screen then Apple logo shows on screen). After this the messages were clear and the Update to iOS 8.3 button was active. Ran the OS update.
Phone and OS seem to be operating OK now although I haven't tried every app just yet.
* As a side note I was updating two new iphones at the same time. The second new 6 was restored from a 5 which was already updated to iOS 8. This restore went perfectly. This might indicate the issue is something other than simply an app download stalling (i.e. it may be something to do with restoring from a backup made with an older iOS than the new device is currently using).
Thanks to all contributors - great community.
Paul