It does not stop companies storing information about people. It just makes them follow rules.
The roles of those involved
The Information Commissioner is the person (and his or her office) who has powers to enforce the Act.
A data controller is an organisation or individual (for example, when self-employed) who determines what data the organisation collects, how it is collected and how it is processed.
A data subject is someone who has data about them stored somewhere, outside of their direct control. For example, a bank stores its customers' names, addresses and phone numbers. This makes us all data subjects as there can be few people in the UK who do not feature in computer records somewhere.