(see previous post!) has been solved, but I will confess to not understanding why the solution works.
The router is supposed to have a default MTU setting of 1500. It was set to 1452 instead. Restoring it to 1500 has made it work again - the PCs will now work with Hotmail et al.
But why?
I suspect, though I haven't actually checked, that the PCs always had an MTU of 1500. All having a lower setting on the router should have done is mean that some packets were split when they otherwise would not have been. But that's what routers are for - to split things up and stick them back together again...
Well, emm to you too!
Unless clients decide (for reasons that I cannot understand, but some do) that the connection is made entirely with the IP option of 'DF' (Don't Fragm ent) enabled. This will break all connections made with a client with the MTU greather than the router's MTU. I've had this problem before, when I had dial-up, and my PC was set for 1500 (Ethernet MTU) and the dial-up had the MTU somewhere in the 700's. For me that problem mostly showed itself in FTP and not HTTP though.