HI everyone, and thank you for your posts. I have now resolved my issue with the very patient and highly competent telephone support of an Apple agent. It seems there is a little known conflict between the current software used by Three network and IOS 9.3.1 which makes a setting which prevents the Three network being 'seen' by the iPad. What transpired is that IOS 9.3.1 seems to have the status of a beta version - did you know that? - and the solution was to do a factory reset and restore using the latest version of 9.3.1. The steps I was guided to take were
- connect the iPad to itunes
- do a complete backup of iPad
- go to restore/factory reset (cannot remember exactly what the right hand button in the upper box on iTunes says)
- when the new software and firmware is fully reinstalled, DO NOT restore backup, because you then restore the settings 'glitch' that caused the problem in the first place
- instead, restore as a new iPad, and then sync the various data and files elements, and other features in the column on the left of the iTunes screen. You can install apps this way, but I was advised - and it is easier - to go the App Store, click on 'purchased' and then choose which of your history of purchases and free apps you wish to reinstall.
- You do lose some settings data in this process (eg I forgot to sync my safari bookmarks), but it does completely solve the problem.
The Apple guy - Alan - was incredibly patient: I had a Windows PC blue screen failure in the middle of it all, so had to reboot and restart the process with iTunes; the total time he was on the line was 2 hrs 20 mins, including the initial diagnosis and then going through all the processses (including discovering that you cannot do a 'restore backup', so we had to go round again, doing a resintatllation of software and then taking the 'set up as a new iPad' route.). Having done this with my own ipad I was able to do the same on my wife's iPad in about 40 minutes.
Hope this is helpful.