Neighbour's conifers are damaging my fence - can I make them pay for repairs?

My neighbour has a row of large conifer trees which are pushing up against my fence and causing damage. The fence is now leaning into my garden and there are some large cracks in the panels. I have spoken to my neighbour about cutting these trees back a few times already, but they haven't done anything about it. As these conifers are damaging my property, is there anything I can do to force the neighbours to cut them back? And other than just asking, is there any option available for making them pay to repair the damage already caused to my fence? Thanks