This is another wrinkle on the existing For a UK rail delay, which train company do you claim compensation from question. Assume you buy a ticket from a London tube station to your destination, which therefore includes a tube journey at the start. (Such a ticket might be a "London U12 to Cambridge", for example)
On such a journey, the tube is suspended, and you consequently arrive at the National Rail station to commence the train part of your journey much later than you should have done. As such, you get to your final destination late.
Were it Train+Train, first train delayed, then the answers in this question would cover it. However, in this case, the initial delay is caused by the tube (operated by Transport for London / London Underground), and not a train. In this case, who should you be approaching for delay compensation? TFL, responsible for the initial delay? Or the rail company who first carried you after the delay, as the first train company you dealt with?
(I tried asking TFL, they said that as I was travelling on a rail ticket I had to contact the first train company instead. Contacted them, they said talk to TFL. I therefore need to work out who should be responsible to re-complain to, since both are pointing the finger at the other...)