Could be a multitude of things. If you're convinced it's not the battery then it'll be something either messing up the fuel/air mixture slightly or spark.
I'd expect you to notice any of those things wilst driving though. When is the fuel filter change on an e9x (if it's a schedule item)? I wouldn't be going ripping out the pump unless you're getting other signs too.
First thing to do as always would be check the codes, then do some air/fuel monitoring if you can
Thanks, I wouldn't be doing anything myself, it's under extended warranty.
I read that the issue with the fuel pump being that when the engine is cool and stationary fuel is sucked away from the engine hence the extra cranks until ignition. And that subsequent starts are fine because the fuel in the line hasn't yet traveled back whilst the engine is warm.
Any particular codes or hidden OBD menu I should be looking at?
Could be an earth issue.
Thanks but I think it's unlikely considering what I described above? with subsequent starts being fine.
there are some evil people at BMW that designed it's fixations!! The dashboard was relatively simple apart from a stupid clip near the passenger side vent, but the centre console was just ridiculous, I had to remove half the cabin to swap it round. At least it allowed me to better route my mediabridge so alls well that ends well 
. Which that Silver X3 pic is not helping 

when I get the car back from the garage I'll treat it to a nice deep clean and a load of gliptone, then crack on with the quad exhaust, all the parts are sitting in my living room begging me to do something with them