Airbus Girl, I would also offer my support for AA, not onlyfor the leg room (I am 6'2") but also for their in-flight service. You may not be aware that ANZ do this route non-stop as well. I am sure someone can tell you whether they are worthy of consideration.
Don't know when you are travelling but, taking Jinkster's travel plans, returns(inc) to LAX from London are showing as around £260 for Virgin, £270 for AA, but nothing under £300 for BA.
Hope you have a great time