Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
If the interruption of your journey is more than 24 hours, then you have a stopover, not a connection. I'm pretty sure that BA will not let you check your baggage through on an itinerary that has a stopover.
You might investigate whether there are any places in LHR that will store baggage for a fee.