Back to my initial situation in which the GPS(s) failed.
It's unlikely to have had anything to do with "Within the aircraft", rain, the aerial and many of the other possibilities suggested, apart from maybe, aliens.
I had two GPSIII Pilots with me, one mounted within the aircraft and connected to an external aerial (but not loaded with my route), and my own GPSIII which was on the seat next to me, loaded with the route.
They both failed at the same time, in different conditions (going north was heavy showers, coming back was dry), on different days, but in the same location. They both recovered in approximately the same locations. The location seemed to be 15 - 20 miles north west and south east of Shawbury.
I use the GPSIII as a "third level" navigation aid, for several reasons, one being that I have had the "Poor GPS Coverage" message enough times not to want to depend on it.
But this was different; both GPSs didn't 'fail' immediately, but started to give incorrect readings for location and Ground Speed, (as stated earlier, over 4000kts

), followed by a message to "Switch off the GPS and re-initialise"). Initially, switching off and on did not work either. Eventually, when about 15 - 20 miles from Shawbury, they both started to work again.
If no-one has had any experience similar to mine, I guess a call through to the Martian invasion force at Shawbury might sort it.