I’m guessing you have a desktop and the printer you mention that are both using wi fi to connect to the BT Hub.
How your mail works (and is set up) depends on a few variables, some of which are listed on the BT help page below
https://bt.custhelp.com/app/answers/detail/a_id/9962/~/how-do-i-set-up-bt-email-on-my-computer-or-mo...I would keep it simple and use your primary network connection to the internet via BT Hub and not your printer wi fi.
Depending on what type of mail service you use there will be options to ‘Get Mail’ or sync with your mail providers servers - often with settings to say what preferences are on when to get or send mail. Check the Help or Settings links that come with your computer or Mail App/ Service.
I use an Apple computer and my old BT Yahoo mail comes into Apple Mail. My Apple computer can connect via wi fi or ethernet cable direct with BT Home Hub. I can always force new mail or sync by clicking under the options under Mailbox when logged into Apple Mail, for example.
Note I switched my printer wi fi off to reduce interference to main house wifi and to reduce overall network security risk. I use airprint facility on printer for wireless connections from iphones and usb cable to main computer otherwise.
Sometimes large attachments will slow an email leaving outbox or if the home wi fi is congested ( a few people watching BBC iPlayer or Netflix on other devices at busy evening times).
Hope this helps.
