There are multiple reports here on FT of people transfering between tickets at LHR BA-to-BA who have had a delay into LHR and not been accommodated for an onward flight from LHR. Some have been on expensive flights to Asia.

Ultimately this is a staff decision and the passenger has not a leg to stand on as the passenger has missed check-in, conformance or the gate as the case may be.

There is some language in the BA COC about notifying BA if it appears that due to circumstances beyond the passenger's control, one won't make it to a departure on time. But, that language does not guarantee a reroute. Moreover, it is not always the case that one is in a position to call BA.