I'm currently being recruited by a bunch of mid sized financial consulting firms in the Midwest. Generally, many of the really large firms directly hire college grads(though many like Deloitte are now looking for masters and specialized analyst training). It's generally pretty difficult to move into a larger or more prestigious consulting firm as an experienced hire, especially with this economy. Even many of the mid sized firms here tend to hire college grads. Most people just gradually move to smaller firms after they accumulate work experience, not the other way around.
It doesn't help that the market for accounting students is incredibly weak, and many candidates who would have otherwise gone for the big 4 route are trying to get consulting jobs lined up. In order to be reasonable competitive at a big consulting firm in this market, you need to have good contacts AND a 3.5-3.8 gpa with reasonable leadership/project experience. The financial market is just such a mess right now, and it'll take a few years before it's cleared up.
This info only applies to the US market. I have no idea how the New Zealand market operates.