I've got a small-ish (30ft) beech tree in my front garden right in the middle of the lawn. Apart from occasional trimming of the branches it's been fine for the first 2 years I've been in my house, but in the last month or two I've had a couple of shoots start coming through the lawn.

I mowed them a couple of times and they came back so I decided I've have to make a slight mess of the lawn and dig them up, when I discovered they are actually sprouting out of some of the main tree's roots (I am sure I give away my limited gardening expertise when I say that I didn't even know that could happen!)

What is my best course of action? Should I try and sever the roots that are causing the problems, or will that damage the tree itself? Is there some treatment I can apply? I don't really want to lose the tree, but the shoots are making my lawn look terrible. Any advice?