I don't think a split at London would have been necessary for a successful claim bc as previously posted, after the train terminated short at Reading I was left with only 28 mins to get from PAD to KGX, which I am pretty sure is less than the min connection allowance. And there is no way for them to determine what time I got to CBG, but as it was not even 15 mins later than planned it would have been a fraudulent claim.
It's true that there is generally "no way" to detect a fraudulent claim with an old style ticket without a barcode, but barcoded tickets typically prevent that (unless barriers are open at relevant locations and there is no check on board).
However, if you had split in London, and then gone and done something in London, a claim could have been successfully made on that basis. (Yes, in theory you could have tried to claim on a through fare on the basis of a break of journey, but good luck to anyone doing that!)
My point, in case it's been missed, is that if you are comparing DR rights with split vs through tickets, there is
no loss of rights with split tickets (quite the reverse; there are
potentially enhanced entitlements to claim, under certain circumstances similar to that described, with split tickets).