I have a Linksys Wireless-G ADSL Home Gateway router.
I had wondered about overheating (it is normally on all the time) so had switched the whole system off for a while. On switching back on an hour or so later everything worked OK and has done ever since.
When I was not getting BT Broadband the computer gave no indication of problems with the router. It gave the usual "Wireless Network Name: linksys Speed: 54 Mps Signal Quality: Excellent" - so I still think it was a temporary BT "glitch".