Anyway, this has a lot of potential for a lesson on etiquette, politics, quirks of British culture, or all of the above. Here's how:
First of all, play the video, and ask students to listen to discover what he's apologising for. It's possible that some students will have seen the clip before, and some of them may even know who Nick Clegg is (although I think in the average class this is unlikely!). You could also ask them whether they think he is sincere, and why.