Is your concern that they won't issue the boarding pass strictly due to the connection time (or that they would issue you one if you had a longer connection)?

I've had several itineraries into LGW or LHR where I've had separate BA tickets, and they've linked them together and issued boarding passes at SFO. My connections have always been longer than 2-3 hours though, so I could hit the BA Terraces lounge before the connecting BA flight.