Myth 1: The DPA says you can't market to people without their consent
No it doesn't. All it says is that you have to tell people when you collect their information that it will be used for marketing. But individuals can object to marketing whenever they want under a DPA right, and electronic marketing (including phone and email) normally requires consent under the Privacy and Electronic Communications Regulations.
Myth 2: You can't process my details without my consent
There is nothing in the DPA that stipulates that consent must be obtained for any specific processing operation. The Act offers six ways in which you can comply, you only need one, and only one of them is consent of the individual.
Some people think that they can dictate to banks and other organisations as to how their information is used, but although there are limited rights to object to certain processing which causes distress, if processing is necessary for a contract, for example, then no consent is needed.
Myth 3: We will never share your details with anyone else
Not exactly true. Someone making this promise might not give customer data to a spammer but they may be forced to give it to the police. Alternatively, the company might be bought, in which case the customer data may pass to a new owner.

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