Firstly, go to their housing officer and make the biggest complaint you can, then go higher in the council and then threaten to take it to the MP and the local Mayor ( council will now be jumping and licking your toenails!)
Ask the council for an incident report book and EVERY time something happens - as small as a loud noise and as big as rats etc NOTE IT DOWN.
Contact benefit fraud dept and report them, contact environmental health and send them photos of rubbish etc
KEEP A COPY OF EVERYTHING!!!!!!! the council WILL lose the originals and this will prevent you going through what i did - i lost two years worth of neighbours from hell evidence becoz council lost the lot and i hadnt got copies!
Everytime you get the police involved, keep a note of the crime ref num, that will come in handy for the incident book.
Speak to one person only and demand that that is the person who communicates with you - that way you have no chance for the council to tell you "I thought you had been told...."
Do any other neighbours have problems with this family? If so, then get a petition going and deliver it to the housing officer, council complaints dept and Police.
Get in contact with the local police station and see if there is a group involved with the family and see if yo can find out what is going on - from experience, if the family are being helped becoz they are the perpetrators, then there is not normally anything you can do about them except complain.
Have you been to see your GP about the stress you are under? that will always help your case as well - if your prepared to give that kind of info out
good luck
Flower xxx