If you are having problems with your neighbours you should try your best to sort it out amicably and in person. Once you start a more formal route things can get messy and what could have been sorted with a chat over a coffee or glass of wine gets expensive and/or the problem gets worse. For example, if you are complaining about noise, your neighbours may increase this just to annoy you!
This is probably the most common complaint people have about their neighbours. A few years ago, when our neighbours were teenagers and their parents were out, they had their music really loud if they had a few friends with them. I went round and complained and they turned it down. The father the following day came round to apologise, I think the kids got into trouble but I think they must have thought it was better to warn him that I had complained. I wasn’t even The Complaining Cow then! We never had trouble with noise again. Obviously I appreciate that other neighbour disputes are not as easily dealt with and I would have preferred to write but sometimes it does just take a little bit of effort.
If, after asking your neighbours to reduce the noise, it continues and they are tenants, contact the landlord if you know their details. Otherwise contact the Environmental Health Department which is able to measure the noise levels. Keep a diary of the noise and use it as evidence to show Environmental Health the extent of the problem. You will need to convince them that the noise is disturbing your sleep and/or preventing you from enjoying your property. Witness statements from neighbours and/or letters from your doctor saying how it is affecting your health all help. Environmental Health officers are able to give an expert opinion on how it rates noise nuisance. Local authorities have powers to seize noise-making equipment.
If the Environmental Health Officer (EHO) considers there is a noise nuisance and has been unable to resolve the matter by discussion, the authority can then serve a notice on the person causing the noise, or on the owner or occupier of the property. If the person causing the noise does not comply with the notice, the local authority can prosecute them. The local authority can also apply for an injunction.
Alternatively you can go to court yourself and get an injunction but get legal advice as this can become costly.
For other complaints about neighbours trees and hedges see this post.