You should be able to set up a SECOND email account on your thunderbird: it will still point to your Plusnet email account, but you set it up using POP3 (rather than IMAP). You'll find the setup details at https://www.plus.net/help/email-guides/how-to-set-up-plusnet-email/
Once the POP3 account has downloaded all the historical emails, then, when you're happy, you can remove the old IMAP account (you'll eventually find that the emails will probably all "disappear"!).
When you set up the POP3, you can tell it how long to leave the emails on the server before deleting them: this can be useful if, like me, you have emails ALSO on your phone. My phone uses IMAP, so sees the emails left on the server: I have my POP3 set up on my PC to delete the emails after 30 days.. which means that my phone gets to see the last 30 days of emails - and anything older automatically "gets deleted" from the phone... so your phone won't run out of space!
MAKE SURE YOU BACK UP YOUR EMAILS on your PC: Thunderbird will tell you where the PC stores your emails: use the automatic backup software on a USB drive to regularly back up the email directory / directories, otherwise you could end up losing your old emails. Alternatively, use "cloud backup".
