The only time I even had a hint of the start-up world was the odd email from the career officer. (I actually remember the SongKick advert. I was really tempted to apply, even though you were just looking for a graduate position. In hindsight, I should have tried my luck :))
What would be useful in promoting the internships would be a start-up demo-day, where bunch of start-ups would come in and showcase their product/vision, development technologies, and any other 'cool stuff'.
Edit: To clarify, rather that a start-up fair, where students stumble about, the demo-day would be contained in a lecture room with a proper presentation and QA session. These types of events were always packed in uni.
http://workinstartups.com/jobs/interns/
possibly you could work with them on this? They seem to be UK based/focused.