Limited experience with the LR4 yet, but in the past I have traced similar issues to this down to something as simple as bad grounds or bad positive connections. Maybe check for corrosion on some of the key grounds, main fuses and other connection points? If there is too much resistance in the circuit, it would look to the computers like the battery is no good.
Also, are you sure the alternator is working as it should? Have you double-checked the voltage across the battery terminals when the engine is running...or can you?
Best of luck, and I hope it’s something as simple as this!
Thanks. Voltage when the engine is running is good (13.7 - 14V), so i'm pretty confident the alternator is ok. Had another look around the battery last night and the was a red positive lea that ran close to the neg terminal - which i've moved away. Lead looked well insulated though. There are so many different red wires on this car its hard to know what's going on. I'll see what happens today.