We are quite good at re-routing delayed passengers these days. There is often an ACARS message (recieved before landing) from Flight Connections detailing any passengers with tight connections and how we propose to handle them. Either met by passenger services and expedited to the next flight or rebooked. We are in a better position to do this as most trunk routes have muliple departures per day. I can get the cabin crew to re-seat some pax in order to have them get off first.
The same holds true for domestic passengers arriving off-schedule at T5 with onward travel.
If the whole airport is closed the system stalls but that isn't the airlines fault and all will struggle........