Hahaha ... Victory!     (phew) It was the decision to test the PC 'disconnected from the web', that led to the solution. ... when the malware failed to appear; it was clear that they were 'getting through' the firewall. You could hear the penny drop... Checking the firewall authorisations, I discovered that they were numerous. ... the suspect ones were 'remote assistance' and 'steam' games. Removing authorisation (un-ticking the box) on all these suspects ... did the trick