ChrisBiggsUK

To bring this particular thread to a close (and hopefully help others in a similar situation in future), a summary;

My 2006 Honda CG125 wouldn't start.  Pressing the ignition merely resulted in a single loud 'click' from somewhere down near the engine.

After trying to jump start the bike, discovered the battery was 20 years old, dead, and couldn't hold a charge any longer.  Battery was subsequently replaced.  This did not resolve the non-starting issue, but the battery needed replacing anyway and this non-starting issue merely brought my attention to the state of the battery sooner.

At the suggestion of one or two people, tried vigorously rocking the bike forward and back while in gear and then starting the bike.  This worked, albeit sporadically, and indicated that it was an issue with the starter motor.
Purchased a new starter motor and fitted it (very easy job on a CG125, may be more difficult on other bikes) and as a result the bike now works perfectly.

It seems that the non starting and single click was (in this instance) starter motor related and as such anyone experiencing similar in the future can (once they have ruled out other potential issues) look at the starter motor as the culprit.  Replacing the starter motor was a very easy job (at least on my CG125 but I assume it would be relatively simple on other similar bikes) and cost me a fraction of what it would have cost to get a mechanic to do it.  If you are able to undo three bolts (in my case I was) then you will be able to change a starter motor.  Look in a haynes manual for your bike (or ManualsLib) and maybe watch a video on youtube and you will see how easy it is to do.

Repair difficulty - Beginner.
Tools needed - Spanner. Coffee/Tea.
Cost of new starter motor (in this instance) - £30