As a tenant you don't really have a recourse to halt what your neighbour is doing, rather your landlord has to take quick and immediate action if he has the grounds to do so. When I went to the Citizens Advice Bureau in the past about fencing, they were very careful to word their advice accordingly and it does appear as if they do not take sides.
One issue they mentioned was that, in the past, people tend to 'guesstimate' where the boundary lines are rather than take accurate measurements and enact a fence accordingly. Hence we may have situations where the fencing is a few centimeters or a few feet off or in worst cases, even more. They may be right, the fence is in their property and hence belongs to them and they have to right to redefine the boundaries.
There are also occasions in the past where people enact fences based on cost and ease, for example if their property is on a slope, they may choose the easiest gradient to enact the fence not bothering whether it is on their property or their neighbours. Such things are of course not practiced now since we have surveyors marking boundaries with pegs but it was not quite so then.
Whatever the reason, if you find yourself greatly inconvenienced by this - whether the hostility of the neighbours, noise, pollution and rubbish etc, you can always choose to move. It is the landlord who is affected by this matter and in worst cases, it may affect his property value if the redefined boundaries are indeed changed. So I believe he should be the one to pursue this matter quickly and hopefully settle it soon.