The same thing happened to my Father recently. It is now going to small claims court as the neighbour refuses to pay compensation as she thinks she's not in the wrong. This was a last resort after writing to the neighbour 3 times to try to get her to make a reasonable offer. It only costs �20 to take it to small claims, which you will get back if successful. The neighbour not only cut off bits overhanging, but up to 5 feet over the boundary! Criminal damage, trespass and theft (as she didn't return the bits she cut off). Good luck!