The answer - which I just found out the hard way, breaking some bits in the process - is elsewhere on this same site from someone clever called Adge. Here is what s/he says:
Make sure machine is unplugged first! Insert a small flat bladed-screwdriver (electricians type) between the body of the machine and the flat surface of the switch button then gently turn the screwdriver so that it pushes the switch button away from the body of the machine. It should be possible to gently withdraw the switch button while in this position. Be careful, the part that keeps the switch button in is easily broken. The same screwdriver will probably fit the Torx screw below. The cable is more likely to be faulty than the switch. Dyson will do this for you cheaply if you call them.
NB I found it was the cable, in the end - it had broken somewhere inside.
Philip
July 2007