You can start by Googling for it, it appears it's related to a malware installation. That it stopped would only be good . . .

Done that.
Could anybody offer any advice?

I have the same problem but just do that, so I tink it isnīt a malware!

I've Googled and Googled but to no avail, so I wondered if anybody here had the same experience and overcome it

I had a look around, and from what I have found, c.exe is part of a trojan called winupdate86.exe that is spread by downloading a bogus patch for Flash. I couldn't find any specific fix for it except people trying everything under the sun to get rid of it, but maybe you will have better luck searching for winupdate86.exe. I feel sympathetic because I spent the past two days getting rid of something on my box that was able to redirect Firefox and was using up tons of memory. I finally tracked down some of the problems by looking at the error logs.