Sorry, Mo; did I misunderstand? I assumed you were talking about junk email but now I see that you only said "mail".
If Royal Mail have been paid to deliver to each address, then they are contractually obliged to do so. You can register your name and address with the mailing preference service - see
http://www.mpsonline.org.uk - and this will, eventually, stop most of the addressed stuff. It takes several months to have any effect and won't stop the unaddressed mail.
For circulars not delivered by the postman, we've found a nice, large laminated notice over the letterbox flap which reads
"No cold callers.
No junk mail.
No exceptions."
does have
some effect and we occasionally see a distributor of junk turning away without leaving whatever it is. (If I see someone ignoring the notice, I'm quite likely to hurl the door open and demand, "Can't you read??!! Take your rubbish away with you and close the gate!")