Thanks for your replies!

On BA's website it says they accept the Amsafe System, which is the same as the CARES harness I believe. Since I can't bring the car seat onboard without buying a separate seat, I thought this would be a good substitute.

After doing some research, I did find out that if you have an infant, you can choose your seats beforehand for free. It wasn't allowing me to do this on the website so I called BA and after a long wait, a very nice CS rep got me bulkhead seats with the toddler bassinet! ^ He also confirmed that strollers are allowed in the cabin if there is room, but if not it will be checked and I probably wouldn't be able to access it until my final destination. I think I may pack my Ergo baby carrier in my carryon as a backup. I wonder if LHR has stroller rentals?

Thanks Squirrel99uk, for the insight about the chances of bringing a stroller onboard. To answer your question, I want to check the car seat with my luggage but am worried about possible indetectable damage, as every family travel website recommends gate checking it. But, it doesn't sound like there is any advantage to gate checking versus regular bag check in this case. Anyone have any packing or car seat bag suggestions? I am planning to buy the lightweight Cosco Scenera car seat for this trip.