so will your mortgage company, if you have one.

Knowing you can't reply Guest all I can suggest is you remove them if you are concerned.

It depends how tall they are and how far from the house. I have inherited a leylandii hedge which gave me some anxiety but my insurance company said it would be ok as long as it didn't exceed 10ft in height and was at least 12 ft from the house. Your best bet is to discuss the problem with your insurance company. I would not have planted leylandii myself but they have made a very neat and effective hedge and it would take many years to replace the it with something else and achieve the same neat thick screen.

I had to dig up a conifer that died in a drought. It was quite shallow rooted although it was about 8' tall and seemed very sturdy. Maybe that was part of it's problem.