Thanks for all the replies. I think the reason that the battery was flat was because the a/c had been used for an infrequent number of (short) flights over several months. The battery would therefore have become depleted and then been left like this over this timeframe. I think there were a few occasions where the engine was cranked for longer than usual due to inadequate priming - it fires pretty quickly if its given about 6 "squirts but is difficult otherwise. So even, say a 2 hr flight following a protracted start which had depleted significant charge, would not return it to a fully charged state. Of course once a Pb-Acid battery is in a low state of charge and then left like that, it will permanently degrade quite quickly - that's the nature of this type of battery. I need to confirm though that the alternator is regulating at the correct voltage necessary for charging, ie about 14V, if it is less than about 13V or so then it will take virtually no charge current (even if flat) but the avionics etc will work perfectly thus disguising the source of the problem.
My backup battery was attached to the a/c battery - the starter was then able to crank the engine perfectly (in fact surprisingly fast) so this proves the link from the a/c battery to the starter is good.
The desire to have a portable "emergency" backup stemmed from some of my flying holidays where the a/c had been parked up for several days, for "peace of mind" reasons. The problems I had recently, reiterated the usefulness of having a relatively lightweight portable supply of power if for some reason one was greeted by a flat a/c battery when needing to return from somewhere. I already carry a couple of Li batteries which I normally use to power other equipment (my Zaon XRX, GPS moving map PC and a few other bits), these are rated at 80A each for 3 minutes use (4 x 3.6V cells) and weigh about 700 grammes per pack. Their voltage can easily exceed 15V off load (too high for a 12V system) but it is not difficult with modern power electronic semiconductors to build up a small converter to drop this to a regulated 12V at a few hundred's of amps (I specialise in power electronics!).
Pilot DAR, I know what you mean about overheating starter motors! In my earlier days I tried to get my old car the last hundred or so metres to home, up a slight incline using the starter, following a breakdown. The soldered connections to the brushes in the motor failed.
Rich