There isn't going to be a problem with that itinerary, though I would say it looks more like 3 journeys than one journey.
Do bear in mind that, while you may claim it as one journey, there are disadvantages to doing so. For example if there is major disruption at Carlisle, and you are stating your destination as simply Manchester, then expect to be told to go back to Manchester! But if you showed the ticket to London and stated you were combining 2 tickets and your destination was London, I expect you'd probably be recommended to use Northern to Newcastle and resume from there. I do not think you can insist on going via a particular route. Also, if you were doing that, you'd not technically be eligible for delay compensation, as you'd be on time at your destination on your journey.
I don't think you can 'have your cake and eat it' so to speak by wanting all the advantages of it being classified as one journey and none of the disadvantages.
It's not an issue here, but it may be with tighter itineraries.
It can be an issue on one ticket too.
For example when some people had tickets from somewhere in South London to somewhere in North London with reservations via Leeds & Carlisle, they were relieved when they were on the Leeds to Carlisle train and it departed because they knew that if they were delayed and missed that, it could put the whole itinerary in jeopardy.
The other day a forum member did Doncaster to a suburb of Leeds via York, but the delay meant he would have missed the last train at York! Given the train made an additional call at Leeds I'd not have wanted to be in that position of claiming the taxi from York!
