Publishing is a highly competitive sector and being able to demonstrate that you have relevant work experience will be a great advantage. Building up a portfolio of work that shows your skills and experience is also important, for example by running or a contributing to a blog where you write or edit content. You can begin building your skills and experience at university by volunteering, doing an internship, having a part-time job or by doing a professional placement.
Unpaid internships and work experience placements are common in this sector and not all opportunities will be publicised, so it's worth contacting publishers directly to see if they can offer you a work experience placement.
You could contact local publishers to see if they can offer work experience by sending a speculative application.