Contacting Your Councillor or MP
Your Councillors and MPs are your elected representatives. They are elected to serve their community and should spend time addressing your concerns and questions (as long as they are relevant to the workings of either your local authority or parliament). You do not have had to have voted for that particular politician in order to expect his/her consideration.
Noise legislation is enforced by the Council. The decisions that they make in other areas such as highways management, town planning and licensing can also have a significant impact on the soundscape. For that reason alone, it is important that Councillors are made aware of what is going on in their community. If they are not made aware that noise should be a priority they will not be able to influence policy or resources.
In relation to your specific concern it is worth noting that their intervention has the potential to have a significant impact. It is important to note that neither are guaranteed to be able to influence any individual outcome; and, strictly speaking, their involvement shouldn’t really make any difference. But it so often does. At the least, that contact from the Councillor is likely to highlight and prioritise your case.
Contacting Your Councillor
In the UK you may be located within an area with a two-tier Council system; consisting of District (or Borough) Councils and County Councils. In that case you would normally contact your District or Borough Council (where they are more likely to be responsible for dealing with noise issues). Where you live in a Unitary, Metropolitan, City or London Borough there is a single tier system.
You will be based within an administrative “ward” that will normally be represented by one or more Councillors. Feel free to contact all of them (although your concern may be channelled via a secretariat to one person).
They should contact you back within a few days and let you know that they will look into the matter. Usually they will request that the appropriate department investigate your concerns or provide feedback on the case if it is something which has already been investigated.
Contacting Your MP
Ministers of Parliament are unable to intervene in your dispute with your neighbour; neither can they interfere with any court decision. However, you can contact them if you feel that your Council (or Councillor) have not provided you with a reasonable response or if the issue is part of a wider problem. In response, they will usually contact your Council and request information or assistance which will bring about a renewed focus on your complaint.