What an excellent idea! In the US if you have arrears of more than $2,500 of child support you can't get a passport until you pay up. I bet it would work even better in the UK where a far higher percentage of people actually travel abroad. The majority of American's would be unfazed by this rule because they never apply for a passport, but for those who want a foreign holiday or who need to travel for a business trip this would work wonders. See the CNN website for a video report on this.
Maybe we could introduce this system here?