How do I find the fault with batteries in Transit 190 (G plate) please?

I have, for better or worse, obtained a Ford Transit van which runs OK, BUT when left overnight or longish periods, when I attempt to start the thing, the batteries are almost exhausted, and it just gives a feeble attempt at turning the engine.
I was told that the starter motor was playing up intermittently when I first bought this van, but it hasn't given too much problems, however, could there be a serious current 'feedback' causing the batteries to fail? If so, what are the likeliest remedies please. (I have changed batteries, still no joy)