Big round of applause for Saab! I set up passwords on the 2 laptops plus the desktop for the relevant user (Mrs B) and the first attempt to connect from Laptop2 to Desktop produced a 'new' login panel asking for user and password and then connected and 'saw'. Subsequent network links worked without the login panel, so it loooks as if the home network function on XP requires user passwords set. Still slightly puzzled how Laptop1 had been able to link WITHOUT a user password but hey, who cares
Thanks to all, especially Saab, for the pointers.