Info on Leylandii Hedges at http://www.scotland.gov.uk/deleted/consultations/leylandii-01.htm
Leylandii have become increasingly popular as a hedging plant over the last thirty years. The plant quickly provides a dense screen, grows well in a wide range of soil and weather conditions and is cheap and readily available across the country. It grows at a rate of 1 metre (3 feet) per year - more than any other hedging plant. To be properly maintained as a hedge it should be trimmed at least two or three times a year. If it is not trimmed, it can reach heights of over 30 metres (100 feet). Other conifers, such as the Lawson cypress (Chamaecyparis lawsoniana) and Western red cedar (Thuja plicata), are also commonly used as hedges, though their use has declined as Leylandii have become more popular. While these other conifers do not grow as fast as Leylandii, they could also cause a problem if left to grow unchecked.
I don't know the extent of damage to the hedge is if the exposed [lateral] root is cut. I know that the more important primary roots usually travels downward and are not exposed.
If you don't want to cut the roots for fear of damaging the hedge, you could dig under the root deep enough to push the root down and cover with gravel and soil and hope that it doesn't surface again.
Another thought would be to telephone tree
arborists in your area and ask the them for their opinion.