Tree roots

We inherited a house a few years ago and have just started redesigning and renovating the garden.  The layout was a large rectangular lawn with several hugely overgrown shrubs in the borders around the edge. There had also previously been trees in the lawn and borders which had been removed, but there are still some remaining stumps (cut off level with the ground) and roots criss crossing the garden just below the surface. We have completely removed most of the overgrown shrubs which had been planted too close to one another and to the boundary fence (ie only 1 or 2 feet apart), and some of which were showing signs of die back anyway, in order to replant the borders.  We have retained a beautiful mature laburnum tree (about 30 years old), and a gorgeous lilac of similar age which is requiring renovative pruning in order to hopefully regain its vase like shape.  Now we're ready to start laying brick edged gravel paths and replant the borders.  However, on starting to dig, just beow the surface is a mass of both old and healthy looking roots and I'm worried about damaging the laburnum and lilac by severing their roots where we need to dig deeply enough to lay the path.  Will severing just one or two large roots (about 1½-2 inches diameter) seriously affect the tree as I would hate to lose it and will have to rethink the layout if this would be the case?  I would really appreciate any advice before I go any further. 

Many thanks, Elaine