Your Engineering email address (email@example.com) is forwarded to your cam.ac.uk address, which will normally be delivered to Exchange Online. If you do not wish to read your mail on Exchange Online then you can forward your mail to another provider. We do not allow people to close their Exchange Online accounts completely as this would also remove their access to Microsoft Teams and other collaboration tools which are essential for their jobs.
Because of the way mail to @cam.ac.uk is routed, you need to change the forwarding in two places.
First visit your lookup personal page. Click the Edit button and you can change the @cam delivery address from Exchange Online to Other, and enter your external address. This will affect only mail sent from outside Exchange Online.
To forward mail sent from within Exchange Online you also need to set up an Exchange Online Forwarding.