Ok, so I've now figured out what the issue is. On the new iPad, if you download a video from iCloud, and select HD you get it in 1080p if it's available. The issue is, and I guess that this is a bug in the software, if the 1080p file is 870 MB and the 720p file is 700 MB, the iTunes app will tell you that the file you are downloading is 700 MB, which implies that you are downloading the 720p version. Once the file reaches 700 out of 700 MB it will continue downloading until it reaches 870 out of 700 MB.
I had always just looked at the file size when the download began and compared it to the 1080p file size which was larger. I therefore assumed that the file I was downloading was the 720p file. It looks like the iTunes app needs to be updated to list the 1080p file size as its target, but otherwise it's working fine.