X5 3.0D E53 2005 Starting Problem

[Rexnest]

Hello all, First time poster so please excuse me if I've omitted any info required.
Every morning my car cranks but does not catch for a few attempts. After 3rd or 4th attempt it catches very quickly and runs / starts perfectly for the rest of the day.
I've only owned the car for 2 weeks and only started to have problems since we've had cold mornings. Car has 120,000 miles but no service history for last few years. Suspect battery / fuel pump relay or fuse / glow plug module, plug or fuse from reading earlier posts.
Any help on how to eliminate any of the possible causes (or any further possible causes) would be greatly appreciated.