Have some excellent news after going through quite a frustrating month and a half to sort out this problem.
To cut a long story short, I tried using a brand new piece of aluminium (without any paint on), as the ground plane, and it seems to work 100% now!!!
I never suspected that the previous ground plane was no good, as it came out of a previous aircraft where a transponder had been fitted. It had a layer of paint over it, (although not very thick) and although I had tried cleaning the contact points, there was still lots of paint on it. (I had even tried to earth the previous ground plane to the aircraft's earth, but even this didn't work previously).
I flew today for about 1 hour, and didn't receive a single error code. Can't believe it. Hopefully the issue is sorted out now. Even flew in controlled airspace and ATC were very happy with what they saw on their screens.
It's my birthday today, so that came as a nice present.
Hopefully this is the end of the matter. Thanks for both your inputs and time to respond. The only time I receive an error code now, is if I touch the antenna when the transponder is on (I was told this is perfectly normal as my body then interferes with the antenna system).
Kind regards, and thanks once again.