Roots from my tree lifting neighbour's tarmac drive

Can anyone advise me on my legal obligations please regarding my neighbour's drive which runs alongside my property?

The root of a young tree growing on the border of my property since before my neighbour had the driveway surfaced with tarmac 3-4 years ago now appears to be lifting the tarmac surface. I can well imagine that branches overhanging a neighbours property would be my responsibility to cut back but does anyone know if the same obligation exists to remove underground roots that have crossed the boundary and are causing damage?

To achieve this effectively I think would involve cutting down the tree and treating the stump to kill the roots to prevent re-growth. It currently offers an attractive screen to our garden and I am reluctant to lose it.