Just a few days ago, I saw the British Airways 747-400 on approach to SAN from my school in National City. It's a magnificent sight; however, it is hard to know what exactly BA plans on using equipment-wise long term.
I recommend the site
http://www.seatguru.com and type in the date and flight number of your particular flight, and you'll be see what British Airways currently knows. If it comes up as a 747-400, well, sorry, that would mean BA hasn't updated their schedules; but if it comes up as a 777, it should show you the type.
The 777-300 with the 4-class service has been seen here many times, as cargo capacity seems to be a major driving force in this route.
You might be able to pay extra and call BA to reserve your seats before the 24-hour check-in time; however, right now even they might not know!
If you are doing LAX-SAN-LHR, you should have an easy transfer at SAN - everything will be in terminal 2. Let us know how the trip goes!!