Let me agree on all counts with PresRDC. I have often resorted to the landside transfer to avoid the mess. Although I understand (don't necessarily agree but do understand) the need for a further security check the problem is with the terrible mismanagement of the security check process as well as the terminal transfer mess. After having sat on a bus outside terminal 1 for nearly half an hour waiting to be let out to stand in a queue for another 45 minutes I decided never, ever to do that again. If your flight gets in before or after the big crush in the morning you can try the air side transfer but during the crush PresRDC's solutions are ever so much more pleasant and frankly the terminal 3 to 1 walk is not so bad and is, in fact, a good way to stretch your legs.

Another alternative but not strictly within oneworld would be to fly to ZRH where you can do an AA codeshare with LX onward. Everything about that experience is many times better than the LHR alternative.