The only OW carrier which protects across separate tickets is AA. BA does not even protect acrross its own tickets.
As OP does not have a connection, but is rather than simply transferring between separate tickets, he is entirely at the mercy of the goodwill of BA and then AY as to whether one or the other rebooks him with or without fee or whether he must purchase a new ticket. This will all be dealt with on the ground with the luck of the draw.