I'm looking for the least expensive way (not via tube) to get from Heathrow to Westminster - as I'll be arriving from long-haul flight from Australia
I don't know this company, but they are quoting around 41 pounds for the one way for up to three people. Seems pretty fair to me and cheaper than a black cab.
Alternative ways would be train (plus small tube journey) or bus. National Express is super cheap, but you would have a long delay in the centre of London.
It depends if its cost or time thats more important. I personally would use the tube into town, head down to Embankment and then cross over into Westminster. about 10 years ago
The cheapest way is to take the bus/coach, but for a small amount more the Heathrow Connect (not Heathrow Express) train is much faster. The coach/trains will drop you in Paddington.
From there it's a short cab ride to Westminster, a slow bus ride or if you change your mind and take the tube the Circle or District lines go straight to Westminster. about 10 years ago