Having now experimented with breaking down the XML file into smaller files, it now seems that the problem is not to do with the author, but a memory issue.
Some of the smaller files upload fine, others are too large. I think it is an issue with my web hosts memory limit (I am using 1and1 and they have said the limit is 60MB), but they couldn't help me any further and told me to check with Wordpress. I think the Wordpress Import plugin is using more memory than my host allows. Can anyone advise at to what to do?