Data protection - need right of deletion

At the moment, data protection law allows you to demand that a company tells you what data they hold about you. (I don't think there's any right to make them correct errors though). What we need is to be able to demand that they simply delete the records. I, for one, want the power to demand that Experian do not keep a file on me (and I have a good credit rating, with "nothing to hide").