BTW Changing in Singapore wouldn't help as it is in the same tax band as Sydney. You need to look for somewhere less than 2000 miles from London to pay the lowest rate.
Across the Atlantic, Aer Lingus with a stop over in Dublin or Shannon for a day on the way over and a connecting flight on the way back would be worth a look.
Many European cities are major air hubs with connections worldwide easily available.
Using your frequent flyer miles gives an idea of how bad the taxes are, just look at the additional charges to fly from LHR compared to other European cities. I came home from a recent holiday via Paris instead of Heathrow, saved a lot of money on the airfare and enjoyed some sight seeing.