Options for email when closing account

[#1]

Hi, could someone please advise on the best way to keep hold of my current Plusnet emails if I have to close my account because of a house move?  I tried importing them to my gmail account, but it doesn't seem to give me the options to do that for an imap account.  I have lots of critical email which I can't lose so would appreciate any help. Thanks.

[#2]

What email client are you currently using, or do you just rely on the webmail interface? If you use a client, there should be an option within it to save all your emails to a file on your laptop/desktop.