a failing battery and fuel economy

I've got a'07 diesel Navara that usually gets around 11 L/100klm fuel economy. (It has a heavy, wind resistant canopy on the back, so not the usual 10L/100klm that most d22 seem to get) Anyway, over the last 3 to 4 months the battery has been slowly dying and at the same time the fuel economy had dropped to over 12L/100klm. I finally bought a new battery and immediately the fuel economy went back to 11L/100klm.
Why is this so ?

I didn't think the load on the alternator would have that great an effect, although it will be partly responsible for it. Imagine, your battery is constantly presenting itself as "deader than dead" and your alternator is going to try pouring juice into it, so it's going to work really hard.

Does that explain a whole litre per hundred km? I wouldn't have thought so, but your alternator should have supplied enough voltage so the rest of the car would operate as normal - which leaves the load as about the only thing that could reasonably explain this.