Loz- I have a 2002 s-type, does exactly what you describe. Just had some extensive body-work done to right-rear, problem appeared about 1 week after getting the car back. Not sure if it's a co-incidence or not, but after seeing your problem described sounds like it probably is.
I noticed that many of the fuses and relays located next to the battery were loose in their sockets; I re-seated them and seemed better until next day when starting problem re-appeared. Did a new battery resolve your issue? Thanks- Tom