But even if the misconnect is 100% confirmed, it looks like they'll still say 'sort it out in London'...

It's presumably an 'excellent' way to save money - the marginal cost of rebooking someone in London is small, perhaps even nearly zero. There's no extra cost in accommodating them on the new BA flight, and most people will take the hotel BA gives them, which might be on a very cheap corporate deal, or perhaps BA block books hotel rooms in advance for this purpose with zero marginal cost (though I might be making this up!)? Either way, I doubt it'll be much more than 50 quid per person, and BA retains the full value of the ticket. Rebooking at an outstation - well, they lose the value of the ticket, plus potentially more, and the expenses might be higher. Much, much more than 50 quid!

And there's another thing - rebooking everyone in London means that management has much closer control over the rebookings process. They can force the staff to screw the customer. This is much harder to do across the globe - especially because in some other countries, BA's attitude will be seen as outrageous, and if there's any scope for staff to be flexible, you can be sure they'll circumvent the restrictions.