Qantas looked at doing this with modified 777-200LR
I vaguely remember reading a few years ago that Qantas was talking to Boeing about the feasibility of using the (then newly-introduced) 777-200LR, with additional fuel tanks, to fly LHR-SYD non-stop. I may be wrong, but I think the main reason the idea didn't fly (so to speak) was that while LHR-SYD was OK, the prevailing winds in the other direction meant that it was just not reliably within range, at least with an economic payload.