Nah, Gower's just misusing the term 'culture' - he's clearly referring to high culture.
It is impossible to claim any place is lacking a culture (although defining it tends to descend into stereotyping and quasi-racism) - Australian and English culture are very similar.
'Culture' is not just the stereotypes of shooting pigs and getting on the piss, nor is it drinking tea in a thousand year old castle. It's democracy, it's the Judeo-Christian ethic, it's humanism, it's the English language. There are so many commonalities between the two that labelling Australia as 'lacking culture' is effectively doing the same thing to England.
Gower does two things that completely invalidate his argument. Firstly, he reduces culture to fit particular stereotypes in order to create a false frame of reference - the eloquent, tea-drinking author vs. the beer drinking bogan (note how he isn't comparing English Chavs to Australian Bogans, nor English intellectuals to their Australian counterparts) - so he can compare British high culture to Australian popular culture, completely ignoring the myriad of high cultural artefacts that have been created by Australia over time (Indigenous artwork, Banjo Patterson's poetry, Dame Nellie Melba), although we have yet to produce a high-class author in the Wilde mould (although in 100 years we may consider Markus Zusak right up there), and that is influenced by the tendency to not accept anyone into the pantheon of greats until they are long dead. We only have 230 years of history, after all.
Secondly, he decides to make the assumption that high culture is representative of a nation's superiority over all others - which is especially problematic when high culture is remarkably Eurocentric by its very nature. It essentially reinforces the quasi-racist view of England's cultural superiority that, amongst other things, led to to colonisation of Africa and the destruction of much of their culture.
The culture of others is not something you deny the existence of or claim superiority over, particularly when you are the classical representation of a group of people who destroyed so many cultures around the world. It's a **** article.