Can UK university require you email from @ac.uk, not OutLOOK?
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.