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I think commonwealth countries i.e. Australia, will get some "home advantage" effect because
a) of the shared culture,
b) the shared ancestry means that they probably have relatives there and
c) the commonwealth young doing their "O.E." in England
all of which makes them comfortable in London i.e. feel like a second home.
(O.E. = overseas experience i.e. a trip to look at the big wide world)
Ever since the English settled New Zealand, parts of the NZ population (and newspapers) have referred to England as "Home" and that was still going on in to the 1950s, even for people who'd never been born in England.
So, I suspect, the home advantage effect won't be as strong for England, mainly because other Commonwealth Coutries will get a share of that home advantage and, because of the shared sporting heritage, they'll be battling over some of the same medals i.e. equestrian and sailling rather than table tennis and syncronised swimming.