Transmission slip on acceleration

[Be em uu]

Hi all,
I have read about a few transmission problems within this forum, but I can't find any who have the combined symptoms of mine.
My 05' 3.0D E53 automatic has recently been showing some strange behaviour which seems to come from the gearbox / transmission system.
When I pull away from stand-still, there seems to be a light slippage and judder from the transmission and sometimes the car revs up before jolting into gear and pulling away, which catches you out when pulling out at busy junctions etc! I have also had it randomly shift down on me a couple of times while driving and rev up before changing up again, under constant power and conditions.
I know there are a variety of problems for this car including the ATF, bearings, oil rings and transfer cases and some to do with the electrical system. My question is; where should I start with dealing with this issue before spending £100's on replacing unnecessary parts? Are there any things that might help narrow down what exactly is at fault, or anyone who has a good idea what it might be? No errors or warnings have come up in the car.
The car runs great otherwise but if anyone’s got any advice, that would be great!
Have a great Xmas and new year anyway guys.