Can an employer access my personal email account on a work computer?

This depends on the personal use policy in your workplace. Your employer should have clear written policies about the use of work systems for personal use. An employer is entitled to view your emails on the work email system, especially if you are using an email address that was assigned to you by your workplace. Some workplaces may have a policy that states the employer can access all email traffic on their system.

However, any review carried out by an employer of your personal activities on the work systems should be done in a reasonable and proportionate way, with justification and by properly authorised people, and may require prior notice.