I believe that at another major UK airport (the biggest non-BAA one should pin it down) the airport ops people who co-ordordinate the response to such problems can call on any company with a suitable tug to assist in clearing a runway. Where there is some warning the tug is standing by near the runway. Getting the runway clear is an absolute priority and I gather that any company that is requested to supply a tug usually drops verything else and does so. There are some insurance concerns sometimes but at least a tug and driver are there on the scene.