Two hours later.
I noticed that my version of Adaware was out of date, so I downloaded version 6. Lo and behold, it caught up with 120 intruders! So I deleted the redundant Spykiller programme via add/remove programes in the Control panel. Even having deleted it, it must still be lurking in the regitry- it comes up every time I reboot. BEWARE- be very careful if you decide to install Spykiller.
a) You will have to buy the programme (Adaware 6 seems better and it's free!), and
b) It sticks like glue, even if you don't want it.
Over to you, Richard!