Richter, making an assumption here, but I think you've misunderstood the FDP scheme. You are ultimately responsible for making sure that you are flying within the legal minimums set out in CAP371 (i.e., you have had the appropriate rest between duties, you are aware of the legal hours you can operate on day x based on report time and sectors to be flown etc), rather than actually logging each and every duty you do.
Personally I make a note of each of my duty starts and finishes, but that's simply so I can check that all my allowances are accounted for.
Regretably very, very few crew really understand the rules around FDPs other than the hours off duty, but blame for this rests equally with airlines who do not go over it in initial training (I know Go-Fly spent a half day going through it and explaining the rules when I started with them). If you sit down and read through the CAP371 rules and take the time to get your head round it, it's actually quite straight forward. I've condensed the rules down into some basic points along with examples to make it easier for me to understand.