I immediately did the thing Mr P-L told me not to do when I spoke to him on the phone later. I shut the computer down - apparently it embeds the nasty bit in the boot system and makes it much more difficult to get rid off.
Luckily, Mr P-L is a computer whizz-kid and could get rid of the nasty bug, rebuild nearly everything and make the computer even better, stronger, faster and it didn't even cost six million dollars!!! I know, the last reference really dates me, for my younger reader, it is similar to a 'vintage' tv programme's opening credits 'The Six Million Dollar Man'.
But, it all took time. So, for several very long weeks, where the younger members of this household berated me and complained about having to change all their passwords, we were without a computer.
The point to my long tale is - if you get such an email - don't open it no matter how real it looks and don't turn the computer off.