I've sorted the problem myself. First I uninstalled AVG. This actually made no difference. Using netdiag I established there was a problem with NetBt. I searched around other forums and found a solution to a similar problem which worked for me as well. I found that the following registry key was wrong;
HKLM\system\CurrentControlSet\Services\NetBt\Parameters\TransportBindName
It had a data value of 1. I changed it to \Device\ (including the two back slashes) and the network miraculously re-appeared after a reboot.