Update:
Being off the VPN made no difference. I closed all the obvious apps.
Pingu brought our laptop up to my 'office' and he got good speed on both Whiffy and LAN.
I then decided to try taking my laptop off the docking station.....
WiFi suddenly double the speed.
Put laptop back on the docking station, shite again.
Did some googling and found some comments on docking stations buggering up the 2.4Ghz band. Switched to the 5Ghz band and bingo, I suddenly have the expected speed!
(I thought I had tried this the last time I had problems and I couldn't get connected but apparently not).
Now, this might just be coincidence and an intermittent fault, and it doesn't explain why it was still shit with the LAN cable connected. But it's working now, will see if it continues to do so ..