To be fair to BA they're pretty good with this kind of thing, I'm fairly sure they would sort me if it went horriblyJust to be clear and warn you ahead of time - they don't because they're (most likely if I understand your post) separate bookings. If you'd booked one flight booking from Athens to Miami with a change / layover in London, yes you're right they'd have to sort it. This is whats called a connecting flight.
But if your Athens flight home is delayed and you miss the new flight to Miami, from what I understand about the rules, that isn't actually their problem as you've taken responsibility by booking flights on separate bookings. This is a 'self connection' and not covered.
So if your athens 1.45pm flight is cancelled or heavily delayed - they have to get you home (to London or whatever airport you booked to?) either on a later flight with them, or an alternative airline + award compensation depending on circumstances and total delay. But they don't then have to rebook you to Miami if you miss that flight. As that will be considered as *you* missing the flight. They might be nice, but they don't legally have to, and ergo prob won't care at all.
wrong.
Very unlikely scenario anyway!!
I just looked at the one way cost of ticket for that Athens to London flight and it's £495 so I'm guessing it's near enough full. So they won't mess with it u less something severe happens.