As CWS says, if your concern is delay problems at the intermediate point (i.e LHR), then baggage is not an issue: they will be tagged and you will collect them at your final destination. The rest of the world is not like the US, where you are supposed to collect your luggage and recheck. There are a few countries where you need to do that when you final flight is domestic but they are the exception rather than the rule. Mostly, you give your hold baggage at the departure point and collect it at your final destination (as long as it is all on one ticket).

[addendum]
Ah just saw your clarification that you were on separate tickets. Yes, BA will not check-through on separate tickets no matter what (well, maybe they will if you are Sean Doyle, King Charles, Pope Francis or Beyoncé but not for mere mortals like us ).

If you are on a through-ticket this time, nothing to worry.