If this happens on the results pages of popular search engines, it can be caused by a "redirect virus."

If this happens on other sites, I wonder whether one of your add-ons might be interfering with the links somehow.

Sorry I forgot to mention that I have checked for the redirect virus and it is not there. I did turn off the redirect and the add-ons but the problem still persists. The one strange thing about my setup is I stay out in the country at a restaurant and my connection is via WiFi to their system and they connect via a 2 way radio link to their headquarters in the city.

Are you using the default DNS servers supplied by the WiFi router? Perhaps try OpenDNS or another provider in case their DNS or upstream DNS is contaminated.

https://store.opendns.com/get/basic (free to use, registration required)

I have been over all their settings and tried various others in the hope to improve the system but it had no effect on the problem. The problem not only shows up in Firefox but with other browsers as well.

It really does sound like malware. If normal scans don't detect it, you might try Kaspersky's rootkit scanner: Anti-rootkit utility TDSSKiller.