Having read many of the threads as my. 2004 td4 77k does the same thing. I only got the car last month and the service book was stamped at 73k. I think all they did was stamp the book, dont think they actually did any servicing at all. Any way Imhave a code reader and it did not show any codes.
Started with draining the diesel water trap, cost zero. Instant improvement but still not correct. wanted to change the diesel filter but. could not do that yesterday (. long story). Cost 16.00 eurocarparts.
changed the filter on the top of the engine and the turbo breather filter.
replaced the air filter, fixed the missing bolts from the back of the air filter housing and refitted correctly. 26 quid ebay
much better pick up and lots cleaner running, need to do the diesel filter today which will hopefully sort the issue.
ALL should have been done at the last service and none have been changed for years.
So my advise is start with a proper full service. Most people's problem appears to be fuel starvation so I stated with the service items. If its still there after, looks like new fuel pump. I will let you know.
if your using a garage, do as have done. Tell them what you expect replacing and you want the old items in the boot of the car when you pick it up. I refused twice to pay for service items because they claimed they had thrown them away.
from 16 to 35 I did all my own work and then moved and didnt have the tools or the garage to do it myself. now back up north I have my tools and a garage again I am doing my own again. my worst garage experiance was after putting new discs and pads on my Merc, I took it for an MOT. got a phone call twenty minutes later telling me it needed new discs and pads. walked back to the garage and asked them to put it on the ramps and remove the front wheels. watched them squirm as I questioned them on thier inspection process and thier reason for new discs and pads.