That depends. If using IMAP messages are on the providers server. Lose touch with the server, lose the mail. POP mail stores messages on your local drive but they are still associated with the email account. If you remove the account from Thunderbird the messages go also.

The best practice in both cases is to make folders under the Thunderbird Local Folders account and copy your messages there. Now they are on your local drive and not tied to any email service or provider. After you copy the messages to local folders make sure you have the entire message vs just the message headers and can open and read them before deleting the originals or discontinuing service with your provider.

Hello Airmail,

Thank you very much for your swift reply. I have made a new folder under the Thunderbird Local Folders account and copied all 6k emails there. I have clicked on a few of these in the new folder; the header and content are both visible.

I shall close the account with my ISP tomorrow!

Many thanks again Airmail.