Working in publishing with a degree (or similar)
A good degree on its own will not guarantee you a job in publishing. Employers want to see relevant work experience and commitment too.
Previous office work and any writing and editing experience you can get will be useful (e.g. editing a university magazine or writing a blog). Or you may consider doing an unpaid internship with a publisher to gain valuable experience. Online and digital experience may help you stand out from the crowd.