The short answer to your question is 'no'. The Data Protection Act (or, to be more precise, a data protection notice) can only be used to stop personally addressed advertisements.

There's a lot more to be said about 'To the Occupier' junk mail. It's worth noting that this type of junk mail also can't be stopped by registering with the Mailing Preference Service; for reasons nobody quite understands the opt-out schemes assumes that people not interested in personally addressed junk mail are interested in advertisement sent to generic addressee, such as 'The Occupier'.

Royal Mail's Door-to-Door Opt-Out will stop items addressed to 'The Occupier', provided that the item doesn't include a postal address. In other words, the opt-out scheme will prevent items delivered by the postman and addressed like so:

Dear Occupier

But any items that include a delivery point will be delivered:

Dear Occupier
DMA House
70 Margaret Street
LONDON
W1W 8SS

In other words, items addressed 'To the Occupier' that include a postal address simply can't be stopped. You could try contacting the sender informally but companies that send this type of junk mail (Virgin Media springs to mind) of course do so because they know they can 'carpet bomb' the country by addressing junk mail 'To the Occupier'. It's a strategy used by companies not interested in using proper mailing databases and that don't care about targeting mail-outs at people who actually might be interested. Good luck trying to get them to remove your address from their database…

Your best option is to return the junk mail to the sender. If an item is addressed you can simply cross out your address details and write something along the lines of 'Junk mail – return to sender' on the envelope. If the item is unaddressed (or doesn't include a return address) you can Google the sender's address and write it on the junk mail ('Return to…').