Single PNR/ticket = not an issue, baggage is always through-checked. The problem is with separate tickets. BA is taking a hard line, basically to get pax to stop buying separate tickets and buy that single ticket (on the premise that this will be more revenue to BA -- almost certainly true, that is the usual reason for a separate ticket). If you cannot reach your baggage for whatever reason, it will go into the lost luggage office at LHR (never to be seen again -- as attested by those mountains of bags piled up at various places, visible from the buses between terminals). Basically not a good idea to be flying on separate tickets when you don't have admission rights to the country in the middle (technically BA can refuse to carry you to LHR and deny boarding for not having the correct visa, as the separate ticket is not proof that you will stay in transit). I suspect your hypothetical example of lacking a visa can never happen as boarding will be denied.