Why can't you just have a laptop next to your work computer to do personal stuff? For many companies, allowing access to personal email via work network is an absolute no-go as it massively increases the risk of data theft. I've worked at several financial companies in my life and they always blocked any kind of page that is designed to store files. Otherwise you get employees that upload sensitive data to some online storage because it's the "simplest" way to continue working from home.

That doesn't mean those companies don't allow personal use but it has to be from devices on another network. Nowadays with most communication happening on mobile devices that's not much of an issue.