1) Don't give up!
Email as many places as possible. In total i've emailed over 60 companies ranging from publishing houses, magazines and literary agencies. Many do not respond, but the occasional do.
If you have any contacts use them to your advantage. Ask people if they know anyone in the industry. It's far better to email someone personally than to an impersonal email such as '@hr.com', which basically any HR member can access - if they access it at all.
3) Websites and Search Engines
Research a lot of websites and check in their 'contact us' and 'careers' pages for any information on the work experience they offer. You can also just search into google something like 'work experience in publishing' and have a look through the links that come up - you may find something interesting!
4) Email vs Letter
From my experience, although it is a costly alternative, sending a letter for the first intial contact to a publisher or agency, can lower the chances of it being ignored. For instance, emails can be left unopened in an inbox for a very long time (I found popular magazine companies can be particularly bad with this), and in contrast letters are generally opened.
5) CV and Availablity
Make sure your CV is fully up to date and that your profile is targeting the publishing industry. Also, try and put a broad range of dates (obviously dates you can do), as your far more likely to get a response. Furthermore, the earlier in advance you do it the better. By April a lot of places have already filled work experience placements until November - there's no harm in emailing or sending a letter months in advance.
Finally, I hope these 5 top tips have helped you. I started my work experience last summer (I had just finished my first year of university) AND I have also managed to gain numerous work placements in that time AND built up contacts, which will hopefully be a great help to me when I graduate.