Turns out there are lots of people having issues with the 5.1.1 update: https://productforums.google.com/forum/#!topic/nexus/Ev4yBSssdIM;context-place=forum/nexus
However because I'm off on hols for a week I'm going to leave it and see if anything changes when I get back. One response suggests it might be because and app has modified a system file:
This is indicative that an app you have installed has modified a system file. As a result the update will not install.
You can install the latest factory image or you can try to see if you can return it to the place of purchase for warranty repair.
Bad form to quote myself I know, but I'm on 5.1.1 at last. Rather than send the phone back I flashed the Nexus 6 with a factory image. Followed one of the guides where you had to unlock the bootloader (and then lock again). Phone is restoring itself now.
Don't know why the OTA didn't work for my phone and why so many people have had problems (the Google Nexus 6 product sub-forum is full of people complaining). Even those individuals claiming to have a brand new phone impacted by the issue.
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