IBM, eh. McKinsey, bleh.
I assume the UK is in the same (sinking) boat as the US. Given that the government isn't able to pay enough to hire top talent, bringing in senior people like Dan Bailey makes begrudging sense.
But using consulting firms like McKinsey almost never does. In the US they are known as Beltway Bandits (the beltway being the ring road around Washington). They exist to give an air of independence to their clients' decisions. But the papers, statistics, and presentations they produce could just as easily be done by civil servants and the imprimatur of Dan Bailey will far exceed that of McKinsey.
Why pay for two expert opinions, especially when only one is truly an expert?