My home was previously three flats and I continue to get 4-5 letters addressed to "The Householder" for the flats. I have registered my addresses everywhere I can and opted out but there does not seem to be a remedy for the addresses that no longer exist.
Most addressed junk mail can be stopped using the Mailing Preference Service and data protection notices. Unfortunately, the exception is junk mail addressed to a generic addressee, such as "The Householder". The Mailing Preference Service makes an exception for junk mail sent to a generic addressee and a data protection notice would be invalid as no personal data is being processed.
You could try returning the junk mail to the senders. Scribble out the address, write something along the lines of "Address no longer exists" on the envelope and put it back in the post. I very much doubt this approach would be very effective though. Senders who prefer to send their junk mail to generic addressees do so because it's the cheap and nasty way of sending out junk mail. They don't have to check if people have opted out and don't have to worry about data protection legislation. That makes it unlikely they will bother updating their junk mail database.
It might be more effective to contact individual senders to explain the situation. If possible, contact them via e-mail; that way you'll have a copy of the correspondence (useful should the junk mail continue).
Other than that you could write to Defra. They have an informal deal with the junk mail industry aimed at reducing waste caused by junk mail. If enough people raise issues such as the one you're dealing with at the moment they might encourage the industry to come up with a solution. You could perhaps suggest that the Mailing Preference Service should allow people to stop addressed junk mail sent to a generic addressee. Defra can be contact via firstname.lastname@example.org.