The local authority have statutory duties in relation to litter, these can be found in the Environmental Protection Act 1990 (google it - Section 89 is where you'll find the litter duties). However a more user friendly guide can be found at
http://www.defra.gov.uk/environment/localenv/l itter/code/pdf/cop-litter.pdf
Which is the Code of Practice on Litter and Refuse. The local authority is supposed to respond to reports of littering within a certain time. This depends on the severity of the littering and the type of area its in (town centre, dual carrigeway, residential areas etc)
The document in the link provides example pictures of the levels of littering, descriptions of the different 'zones' and also the response times for each level of littering.
Spend 15 minutes reading the Code of Practice, then give the relevant department at the Council a ring (they're often called the StreetCare or Environment departments). You might get further if you know the standards they *should* be working to.
I'm afraid I don't know what you can do about the verges but I would think its also a Council issue - probably the highways dept. Although if you can identify the tenants causing the damage it may be possible for the housing officer to speak with individual residents.