I'm in the same situation as you. I'm arriving from Toronto to LGW early morning around 10AM, then have to transfer to LHR for my QR to Doha flight which is at 9:55PM.

I called Qatar's hotline and they did mention that at LHR, the check in's generally open 4 hours before flight departure. With that said, the agent suggested that once I arrive at LHR, to check in my baggage for my flight (same airline just different time of departures) and then feel free to go to the lounge inside or spend time in the city.

Point - if there is an earlier flight, you can try checking for your flight at the same time.