Can UK university require you email from @ac.uk, not OutLOOK? I have children who attend UK universities. Because GDPR, the university forbids email forwarding or accessing @ac.uk on Outlook. However, the university's @ac.uk system is more user unfriendly than Outlook, and they prefer to use Outlook! 

Some instructors and department admin agree, and are willing to email both her Outlook and and her @ac.uk account. However, others order her to email them from just her @ac.uk, and refuse email to her Outlook account.


Should she be required to send email from just @ac.uk account? 
Because of freedom of speech, we can't force people to email her Outlook. With that said, how can we sway instructors to include her Outlook account as well?
I am afraid that your question is based on a wrong premise, which I will try to correct.


Most (if not all) universities in the UK give their students and staff an email address in zone .ac.uk.
Most universities in the UK provide their email via outlook services. Outlook is a product/service offered by an international company which has physical servers in many countries, including UK, which make them GDPR-compliant. They can even install a server on University premises if required. 
University staff are discouraged to reply to student emails coming from external addresses. The reason is GDPR or pre-GDPR data protection measures: there is no simple way to check whether an email from john.doe@obscure.server.com really comes from John Doe. That's why staff will usually only respond to university email addresses, which can be verified by University IT.
You can configure an email client (e.g. Outlook) on your computer to work with a university email address and it will be as friendly as your personal email.