Probably the most sensible / effective thing to do is to ask the residents to take responsibility for dealing with the junk mail. If you could try to find a resident who's willing to put all the junk mail in a recycling box then that would reduce the health and safety risk (and presumably prevent the communal areas looks like a dump).

There are a couple of things you can do to reduce the amount of junk mail being delivered to the properties, but again you'd need the co-operation of the residents:

• The vast majority of unaddressed mail (i.e. leaflets, free newspapers etc.) can be stopped by signing up to Royal Mail's Door-to-Door Opt-Out and putting anti-junk mail signs on the letterboxes.
• Addressed junk mail can be reduced by getting the residents to sign up to the Mailing Preference Service. As the landlord, you could register previous residents with the Mailing Preference Service, which should reduce the number of adverts addressed to people who no longer live at the property.

In addition, you could try to get the local council involved. If you can make the case that the junk mail is a fire hazard and a health and safety risk then they should at least look into the issue. Perhaps you could even ask the fire brigade to visit the property to identify any risk – if they'd say the junk mail is a fire risk then you'd have a strong case for the council to get involved.