I uninstalled and reinstalled the app, after going through System, Settings, Storage and specifying that new apps should be installed the phone's hard drive rather than the SD card.
I then had to go through the setup process again, but that took only a minute or so with my Barclays debit card and PINSentry device.
So all is working again. Only slight downside is that I have lost all my saved payees, so they'll need to be set up again as and when I need to pay them, as there doesn't appear to be any way to transfer them from Barclays Online Banking.