Ok, here is the update.
I spent about 70 minutes on the phone with UA and the nice agent told me that she managed to get me all the way from SYD through to HEL for a mere $1701 and the fare was
YHOX instead of my original BHOX. A confirmation was sent to me via e-mail.
Today, I rang again to enquire whether the gap payment between BHOX and YHOX had been processed. To my shock and horror I was advised that my original ticket was cancelled and refunded and that I was holding no confirmed reservation at all.
To cut the long story short, I was given a new booking number and have currently the same itn as originally - SYD-SFO-LHR. The agent told me that since UA does not fly past LHR then he cannot book me anything further either. I know that this is not true but since this guy is well known for his nasty manners and mean spiritedness then I did not argue with him.
I called again and got off the 80 minute conversation which provided no positive results at all. The YHOX fare which I was quoted yesterday at $1701 had mysteriously gone up to $2529. Talk about inflation!
So, I am back to square one.