That's because the popstate file contains data for a specific pop server. Since you changed the server name, a new popstate file was generated and it doesn't include ANY of the data from the old server name's popstate file. You can't avoid this, because as far as Tbird is concerned, it has NEVER downloaded any messages from the new server.

Thanks for the reply Stans, much appreciated.

However, this was an IMAP account (not POP) and I don't have any new popstate files in my profile.

It's worth me noting that my iPhone was able to accept the new account details without duplicating any mail.

In that case, Tbird still had its locally stored copies downloaded from the old IMAP server and is reusing the same mbox files with the new server. You can avoid this next time by deleting mbox files so that Thunderbird can recreate them with messages from the new server. iPhone (and other mobile devices) do not synchronise all messages for offline access like desktop IMAP clients do, so this doesn't count as a proper comparison.

Thanks for the suggestion. But why would it be a problem using the same mbox files with the new server? Every time it connects, it must have some way of comparing a local email with a remote email and detecting whether it needs to make a new local copy. Why would me changing the address it connects to, affect the way it detects mail it already has locally?

Every time it connects, it must have some way of comparing a local email with a remote email and detecting whether it needs to make a new local copy.

It doesn't. Thunderbird doesn't have an inbuilt mechanism for avoiding or cleaning up duplicates, as far as I know.