Our interview takes place near Covent Garden in the just-opened London branch of the public affairs agency he and compatriot pollster Mark Textor founded three years ago in their homeland.
His arrival nine months ago to lead the Tory campaign attracted much media curiosity - he had after all masterminded four successive election victories for Australian PM John Howard.
During the 2001 election, Crosby and John Howard were criticised for responding with a harder line on immigration amid allegations (which turned out to be false) that asylum seekers tried to blackmail their way into the country by throwing children overboard.
But Crosby is no limelight junkie. 'I was surprised at the interest in me, I've been somewhat bemused by it all,' he says in a laid-back drawl.
'I'm not big on gurus or celebrities like Alastair Campbell. The people behind the scenes are the people behind the scenes.'
To his obvious frustration, he notes 'there is more interest in process here (than Australia). There's a lot of interpretation and commentary around the campaign to the exclusion of focusing on the true messages'.
He says the Tories' focus on gypsies was interpreted as a race issue but its 'true message' was to show Britons that the party would 'reward the right sort of behaviour and not reward the wrong sort of behaviour.
These people don't pay their local taxes, they turn up and make people's lives difficult'.
Crosby says he is struck by the 'dominance of print media politically' over here, and the 'partisanship of the media', reserving some veiled criticism for the Beeb: 'The BBC comes from a socially progressive value set. That sometimes leads it to view the Conservatives in a particular way'.
Now 48, Crosby grew up on a farm in south Australia: 'People there are pretty independent - you're miles from the nearest town and have to look after yourself.' He won a high-school scholarship and read economics at Adelaide University. He stood for the (right-of-centre) Liberal Party in 1982 but lost, so a career in the backroom beckoned.
His proudest achievement is his family and 'having a normal family life' (married with two grown-up daughters). But he evades a series of questions that dare to probe a little deeper into his persona. Biggest career mistake?
'Well, I don't believe in saying I shouldn't have done this or that.' Toughest moment in the general election? 'Don't know... I'll come back to you.' Okay, who do you admire? 'Lots of people, no one I admire most.'
This could be part of the slipperiness that comes with years of political spin-doctoring. But Crosby later admits: 'I don't enjoy talking about myself.'
So what is Crosby Textor's offering? 'It's not lobbying,' he says. Briefs for clients include 'more effectively communicating with investors, defending against hostile takeovers and helping industry bodies lead on certain debates'. Clients remain top secret.
Crosby plucked the Conservatives' head of research George Bridges from Central Office to be MD of the London operation. Global expansion and mass hiring are not on the agenda, however. The agency makes a virtue of making its 'principals' available to clients.
Crosby is now spending the majority of his time back in Australia. He points out that with Labour clinging on to 32 marginals by a total of just 29,000 votes after 5 May, it will only take 14,500 switchers to all but wipe out its majority. Would he relish the chance to finish the job for the Tories? 'I would consider returning to help them,' he says.
To his likely bemusement, the UK media could one day rekindle their fascination with this enigmatic Aussie.
1986: Government affairs officer, later joint ventures officer, Santos Petroleum
1991: State director, Queensland Liberal Party
1994: Deputy federal director and deputy campaign director, Liberal Party of Australia
1997: Federal director and national campaign director, Liberal Party of Australia
2002: Joint MD, Crosby Textor
2004: Campaign director, Conservative Party.