Andy Packer,
That is a first, I thought the Series 4 would be long beyond the fun we have with the S1 starter. Over time posts for the S1 have suggested a combination of the S1 PC925 battery having thin lead plates prone to cooking from certain conditioning chargers and engine heat, I take it the S4 has something more robust in the way of a battery, cooking of the starter motor from engine heat. Moisture, S1 more reliable when kept moisture free. Depletion of battery charge via clock and radio, car best kept with power disconnected. Lack of use of car adding to various starter system parts getting a light corrosion. Of course ensuring a good earth and clean terminals are standard to any car and are more likely a S4 issue than the S1 stuff I have quoted. Hope you find a cure.