You can only trim branches that encroach on your side of the boundary legally speaking. I would go over to the neighbour and see if they are willing to have the trees trimmed/cut down. I would not mind if a neighbour asked me. If reluctant then offer to help pay for it and perhaps show them the effect of the trees on your garden.

You have no case legally for insisting they trim the trees so that you get more light. However, both the trees are far too close to the foundations of your property for comfort and are, in fact, a high subsidence risk. You might be better seeking a way to advise them that you have problems with the foundations which appear to be caused by their trees, or that you may have such problems if they don't do something about it, and when/if you do, they will be liable for the damage. Insurance companies regularly dig out and extract roots to identify them, then sue the neighbour to recover the costs involved if its proved to be their tree which caused the problem.

Thank you for your replies. We have already offered to share the cost. They are very much aware that our garden is shaded but still are unwilling to have anything trimmed despite being involved in the discussions with the tree surgeon. We will however speak again with them along the lines suggested by Bamboo. Thank you