For those who don't know, the UK rail network was largely privatised in the 1990s. Whether or not rail privatisation is a good thing is still very much up for debate, but even most pro-privatisation people feel the way it was done wasn't the right way! One upshot is that most non-trivial journeys will involve travel on trains operated by more than one train company.
Let's consider a hypothetical journey, A to D with a change of trains at C. The A-C journey is to be operated by TrainCoA, C-D by TrainCoB. Unfortunately, the A-C train is cancelled, so you end up getting a later train A-B, another B-C, and then a later train than you'd planned C-D. Oh, and then the C-D train you eventually caught was very late too. Everything was bought on a single ticket.
In this situation, which train company do claim compensation from? TrainCoA, as their initial cancellation was your first delay? TrainCoB, as their C-D delay was the largest delay on your journey? TrainCoC, who ran the A-B journey that you got instead, as they were the first company who's trains you managed to take? Or can you take advantage of the privatised nature of the system, review the compensation policies of all three train operating companies, and apply for compensation from whichever company has the most generous compensation for your sequence of delays? (Many of the companies have different minimum delays before compensation is due, and different exclusions on what their delay compensation covers....)