Shot in the dark but,
The PC has a wireless NIC.
Apparently not, but good thinking.
I have one PC connected to the router via cable
Connect the PC to the router and all is good.
Which is it?
Normally the PC is connected to the router. For test purposes I disconnected the PC while it was on. The PC has to be on AND connected, in order for the wireless to perform normally. If it is either off, or simply disconnected, then the wireless is so slow that things don’t connect or take ages.
I’ve since tried changing the channel on the router to 6 (from auto) and things seem much improved, though I’ve no idea why.