Effectively it is assumed consent - in many other European countries this is unlawful, customers have to give explicit consent to sign up to these things.
Worse, a lot of these outfits share their data, or they are one part of a much larger organisation.
Once you "bite" you can receive endless amounts of this sort of stuff.
Being on the Mail Preference Service gets rid of some, but sadly, if you buy and don;t tick that box they have your "consent".
The best way to get removed is to write to them and say that you want your name to be removed from their mailing list, and quote that this is your right under the Data Protection Act.
There is no commonsense involved, because all the mailing lists etc are automated, and the computer can't differentiate when it;s addressing to someone in a care home. It's just another address.