It genuinely doesn't matter who you claim from, as per NRCoT the claim will be passed to whichever TOC is actually liable, which is not the same as the TOC who would bear the most common sense "responsibility" for your delay.
As mentioned, my experience and that of the OP (and others) is claims are rejected on the basis that the TOC thinks another TOC is liable, and are not forwarded, leaving the passenger caught in the middle. That's why the OP asked for advice. Explaining what should happen and pretending that it always does, doesn't necessarily help.
You could miss your train at Kings Cross because of SWR recovering from a fatality and end up on the LNER 30 mins after (current DR entitlement: 25% of your return ticket), and then that train ends up breaking down and is now over 2 hours late. SWR have to pay that one - the full amount 100% of your return, even though it wasn't their fault you were late and it certainly wasn't their fault you ended up getting further delayed by some other company's incompetence or poor performance, quadrupling their liability to you. That's just the way things go and it isn't the passenger's concern. It all evens out in the end.
Perhaps I oversimplified for the sake of brevity: I'm not making a judgement on which company (if any) has cocked up. I'm proceeding on the assumption - as one has to - that if a TOC's train is late, it is deemed responsible for compensating the passenger (which doesn't mean it is actually to blame, nor preclude it seeking compensation from a third party if the industry arrangements permit it - though hopefully in the brave new world there will be some acceptance that these things don't really matter). So, I think we're on the same page mostly.
All you're saying that I don't particularly agree with is that where a delay on an earlier leg simply shortens my waiting time to begin the next leg of my journey but doesn't put me overall behind schedule, I'm supposed to allow the railway to pretend the operator of the first leg is responsible for a subsequent delay
even if that reduces or removes my entitlement to compensation. I just think that's bizare - once I begin the second leg of my journey on schedule, at that point I know I will have no delay repay claim against anybody unless something else goes wrong. It's more than just counterintuitive to say that whatever else may go wrong after that point, isn't the cause of the overall delay - it is factually incorrect.
What if the first leg is Grand Central and the second is LNER? This isn't cakeism; I've already said I wouldn't claim in the reverse situation i.e. I wouldn't claim against a DR15 operator for an overall 15-29 minute delay if the delay on leg 1 - the DR15 operator's service - wasn't material to my actual arrival time at my destination and the material delay occurred on leg 2 which was operated by a DR30 or an open access operator.
I can agree it doesn't really matter if the OP's claim is paid out by LNER or SWR, although since the claim wasn't forwarded, the OP is left wondering which TOC to pursue or whether to pursue both. Hopefully it won't come to this, but if the OP needed to complain to the Ombudsman, they would have to name one TOC on the complaint form, and the Ombudsman would only be able to consider one complaint at a time about each of them. I suppose a passenger could complain about both in parallel, and invite the Ombudsman to adjudicate and direct one of them to pay. The idea that the passenger never need worry about who is liable is very nice, but it's not how things are sadly.
