Yes ! I finally got the remains of the snapped bolt out.
I figured out why it was so difficult, and it seems like you could be having the same problem. The existing drill bits I was using were absolutely rubbish, they might as well have been made of chocolate for all the impact they were having.
I started using some different drill bits and hey presto, it went through like magic !
What you need to do is start with a relatively small bit, e.g. something like 3.5 mm, and don't put too much pressure on it. Then go up to 4mm, then 4.5mm and so on, up to about 5mm or 5.5mm (mine went at 5mm).
You need some decent HSS drill bits designed for metal. My original bits were Rolson HSS ones from Maplin, but as soon as I started using them they went blunt, and I broke several. Compare one after you've been using it with a new unused one, is the end still pointed ? I bought some Kamasa ones from Robert Dyas and they're a huge improvement, the difference is like night and day.