OK. It looks like the scope is acting as an aerial when the pulse generator is connected to it. There must be some kind of leakage when connected to channels 1 & 4, but not when connected to 2 or 3.
If I hold the pulse gen about 1metre from the scope & touch the centre pin of the BNC on the pulse gen with a short screw driver, it kills the wifi connection. Of course, the fast rise time pulses will have plenty of harmonics, but I didn't think they would extend into the 2.4GHz band with enough strength to wipe out the wifi signal. The scope is only about a metre from the router.
I might probe around with the spectrum analyzer later.