More than likely if they were doing ok before Cread. How long ago did they plant the hedge, & what was there before it?

What variety of laurel is it? If it is Prunus laurocerasus, the cherry laurel, then it can become enormous if left. It will be taking the light and moisture from your garden. Firstly you need to find out what the eventual height that your neighbour intends to let it grow to. I would also cut back any roots that come into your garden to lower the competition for moisture. You can then re-think your planting scheme. The senario is not all bad. If your soil is acid, then Camelias, Rhodos and Peris will do well in the new conditions and your Hydrangea will still thrive.

Sadly I think you are going to have to learn to live with it, if you want to stay on speaking terms with your neighbours.