I had to book an EDI-LHR connection separately when we bought CW seats on the 2for1 promo last year and I contacted BA regarding what would happen if the EDI connection was late/cancelled. I was told that while BA would do their best to help, because it was on two separate bookings they wouldn't be obliged to reschedule my flight to Calgary and therefore they couldn't guarantee it (which was what I expected them to say). It may be different if you're a F customer, I don't know.

Anyway based on that advice I went for the 4 hour layover option with the 1145, so there was room for us to be shifted to the 1345 if the first was cancelled. In the event, things went smoothly and we spent the 4 hours in the lounge at LHR, but I was much more relaxed knowing we had that slight safety net.

I also asked them about the additional CW luggage allowance vs the domestic entitlement and they advised me to let them know a few days before the flight and they would speak to EDI staff to ensure there wasn't an issue checking the additional case(s). In the end I didn't need to do this.