ddeOapb is spot on as far as I can see. I can confirm that the UK register of civil aircraft is a public register which the CAA has to make available. It is also, because of this, exempt from the data protection act. As far as people using it to track down celebrities I think that's a bit far fetched. Apart from the fact that most 'celebrities' will either have their aircraft registered abroad for tax reasons for the same purpose if they are registered in the UK they will definately be registered to Ltd companies.
This information has always been available this is just in a differnt format. As far as I can see the CAA can't win. Most of the time they get blamed for withholding info or charging for it. As soon as they make something available for free they get it in the neck for that as well.
By the way I'm sure no burglers had thought of it until you mentioned it here!!