You don't say how long you've lived there, or if the trees were there prior to you moving to the property.

However, if the branches hang over to your side of the fence, you should be allowed to trim them back, but it's best to have a word with your neighbour first, they might even be willing to have the trees cut back professionally.

If the trees are well established...and were perhaps there when you moved to your property...and roots are not undermining any parts of your property then it's unlikely you can do much at all...apart from trimming overhanging branches.

It might be worth you checking with your local council, if you can't come to some agreement with you neighbour. Something to bear in mind is that many trees over a certain girth are protected.

Unfortunately there is no 'right to light' in your garden. If these are deciduous trees then even if they were planted after you bought your home there is nothing I know of that you can do. On the other hand if they are the dreaded Leylandii there are rules about the hight - usual around 2 metres.

Take care and send in some very good photos so we can all see what the problem is. In a previous house , new neighbours didn't want their three 60" Leylandiis. When I moved in some 25 years earlier they were only 20' tall. My neighbour was old and very nice so we put up with the trees. The new neighbours paid for two to be cut down and I paid for the other.
It was worth it. Southportsmith