Actually, Australians have such a tendency to do the thing you've written, that they invented a term for it: tall poppy syndrome. So I'd have to disagree with your attempt to differentiate Aussies from British - it's the same mix of bias/arrogance and pride as any other sporting nation, with slightly more arrogance due to them expecting success.
As an example, I was living in Perth when Scotland had, at that point, won more swimming medals at a Commonwealth games than Australia, and they were spitting with derision that Scotland could better them. And when Scotland had Australia at 5 wickets down for 30 odd runs in a cricket match, they cut regular television coverage and were almost ready to declare a national emergency (before Australia recovered to win comfortably!).