I am trying to cancel a paid Dropbox subscription, but the email linked to the account belongs to my old company - so I can no longer access it.
You'll need to contact Dropbox Support directly. Visit the Support page while you're NOT signed in to a Dropbox account, including these forums, and you'll see an option for Billing issues. It's best to use an Incognito or Private browsing session to make sure you're not signed in.