I quite agree with what Yorkie has posted, if there are no facilities to purchase tickets at the station where you began your journey, then you should be able to buy on board, although if there is no ticket inspection, either due to short journey time or the train being busy, or most likely a combination of both this should carry over to sunsequent train on the journey, which is my interpretation of KWVR45's quote from the NRCoC. I do agree, however, that in cases where there is a long connection time, it would be more reasonable to expect passengers to buy at the interchange station, but then when writing such conditions it would be difficult to draw a line.
Now a question. Does anyone know Northern's policy on this when it comes to split tickets. In the near future, I will be travelling from Burley Park, interchanging at Leeds intending to buy a pair of split tickets, with the split being at an intermediate calling point on my second train. Both trains are operated by Northern. Burley Park is unstaffed, as far as I know there is no TVM there, but even if it is it would only be able to sell my first ticket. In the quite likely event that the guard doesn't get round to sell me a ticket (I will minimise this risk by boarding close to the guard, most probably at the back of the train) and I don't get time to use the excess fare window at Leeds, which is possible because it is only something around a 10-15 minute connection, would the guard be obliged to sell me both tickets with a YP discount? Also, would the first guard, or the excess fares window all be obliged to sell me both tickets? If they sold me just the first one, would I be able to buy my second ticket with discount on the train, provided I asked the first time he checked tickets, which would almost certainly before the station where I change tickets?. Thanks for any responses.