Little bit of a grey area. I don't know what data you don't want them to hold? As far as I'm aware they don't have to destroy data (unless perhaps what they hold is incorrect). They are also at liberty to charge you for showing you what they hold on you (up to a maximum of �10) which you may or may not think is worth it. They don't have to show you anything they hold however unless its held as computerised data or in a 'relevant filing system'. If they just keep stuff haphazardly then, legally, they don't have to show you what they hold.
Probably not what you wanted to hear, but this is the Data Protection Act 1998 and it's a bit grey in some areas as I've said.