Fox theorises that much of what she terms the English 'social dis-ease' (her central defining characteristic of the English) derives from living on a crowded island. An obsession with privacy, rigid rules of fairness and courtesy (an overuse of please, thank you and sorry; a notorious obsession with queueing), a preference for understatement and modesty, all might plausibly spring from a need to protect oneself from the proximity of others. (Indeed, Fox sees interesting parallels with Japanese society, also a crowded island.)
This is something that probably hasn't travelled to Australia -- with plenty of room to spread out, Australians can afford to be more friendly (not a universal rule, I am well aware, and one mostly applied to 'people like us.') But an emphasis on humour, which Fox sees as a distinctively English way of being in the world, I think has travelled down under -- self mockery, taking the piss, irony, wordplay, all seem just as characteristically Australian as characteristically English.
Some aspects seem more uniquely English, such as a preoccupation with class markers (not defined by money or occupation, but by language, taste and attitudes), and a tendency to 'Eeyorishness' (as indicated by the phrases 'Typical!' and 'Should have known...'). But the typically English social awkwardness and discomfort with expressing emotions publicly, certainly seems to have been passed down through my family. Typical. Should have known.