Actually, the Data Protection Act deals specifically with the storage of personal data with particular emphasis on electronic storage; if I do not keep any there are no data protection issues.
But, yes, it does seem a bit like semantics; however, the act does allow for simple data processes for business purposes without the need for registration, and the storage of a customer's name and address, solely as part of a sales invoice, falls under that category. On the other hand, storing information about a person, based on identity or some personally identifiable characteristic does require registration.
Put simply, as it was once explained to me, if I keep all my sales records organized by date or invoice number, say, I probably do not have to register. But, if they were organised by customer name then I certainly would. Semantics, perhaps, but isn't that what interpretion comes down to?
Incidentally, I did not mean to suggest, or imply, that anyone should totally destroy their sales data - that would just be silly.
And, by the way, I have been running an online retail site for over five years now without using customer accounts or finding any need to store customer information. Just keep a copy of the invoice - it's how we used to do it in the days before computers! - and clear the database regularly. (of course, it all depends on the type and size of business, but it works fine for me.)