No compelling business case yet?
If they need McKinsey to help them create a "compelling business case", then isn't that akin to saying "Cloud/Hybrid Cloud is the answer, now what's the question?"
I'm not saying it isn't an answer, but if they don't have a compelling business case in mind already then surely all McKinsey will do is create a compelling business case for the Cabinet Office to blow £3m with McKinsey over 8 weeks.....?