Provided you have tried and exhausted all other avenues for resolving their hedge dispute, you can take your complaint about a neighbour's evergreen hedge to your local authority - your district or borough Council.
The role of the local authority is not to mediate or negotiate between the complainant and the hedge owner but to adjudicate on whether - in the words of the Act - the hedge is adversely affecting the complainant's reasonable enjoyment of their property. In doing so, the authority must take account of all relevant factors and must strike a balance between the competing interests of the complainant and hedge owner, as well as the interests of the wider community.
If they consider the circumstances justify it, the local authority will issue a formal notice to the hedge owner which will set out what they must do to the hedge to remedy the problem, and when by. Failure to carry out the works required by the authority is an offence which, on prosecution, could lead to a fine of up to £1,000.
An overview of the high hedge problem is found at http://www.communities.gov.uk/planningandbuilding/planning/treeshighhedges/highhedges/. (The Office of the Deputy Prime Minister has subsequently become the Department of Communities and Local Government).
Guidance as to what constitutes a problem hedge can be found at http://www.communities.gov.uk/documents/planningandbuilding/pdf/hedgeheight
You can contact Communities and Local
Government about high hedge matters at
hedges@communities.gsi.gov.uk