Alastair,
Welcome.
I would check first to see if you need to trickle charge. I've not had any problems with mine in the 2 years I've owned the car. But others have so it maybe an issue with each car. Can you check with the previous owner?
Regarding servicing its recommended every 6000 miles or annually. At 1600 miles I doubt yours has even been warmed up. I've just sold mine and that was an on a 55 plate and had covered 35,000 miles, so you'll have some catching up to do.
As Mr Tony said we need