Its simple trigonometry, Dave.
London is 0 degrees West/East. It is 51 degrees north.
Sydney is 151 degrees East and 33 degrees south.
Each degree is 60 nautical miles. Make a triangle.
angle 151 degrees. sides are (90-51) x 60) and ((90 x 60) +(33 x 60))
Bit of trig later
9,495 nautical miles. There is a fair bit of rounding on my part not using minutes etc but you see how its done. The round earth value is 9,174 nautical miles.
Hardly impossible to make a calculator, is it?
However, I don't want to generate all the answers. I'd rather the community got together and debated the calcs and the mathematics. This isn't Thork's flat earth society.
If a formula is arrived at, I'm sure me or Pizzaplanet can convert this to javascript or whatever their preference is.