In a larger sense this is partly to blame on a problem that has nothing to do with the Conservatives, as the new position of London mayor still gets the kinks worked out. The position of mayor is essentially an American system that was shoehorned into British politics in 2000, but in some aspects they seem to have not grasped it properly. An American-style complete change in administration takes time to work out. That’s why the US has its elections in early November, and the winner doesn’t take office until January. That gives them several months to put together an administration and ensure an orderly transition. Here, Johnson took office just days after the election, and had to hurriedly select administration professionals and advisors without proper background checks.We've already seen this to an extent with candidate selection - the British system generally expects politicians to work their way through the benches, not jump straight in to a high profile position from outside politics, Arnold Schwarzenegger style. For borough councils an elected Mayor just about works because it's a natural extension of the role of a councillor, although there have been many independent Mayors from outside politics. However for London it becomes hard to attract candidates in all parties as it's a diversion from a parliamentary career (and indeed takes one out of the House) but candidates from outside the regular political classes are hard to recruit.
And we see it again with the lack of a transition period. This is a relatively new thing in British politics - in past decades the outgoing government often took a few days to resign and the incoming one had more time to put together an administration. But nowadays a new government has to be put together by the new Prime Minister within hours of the election result. Because virtually all the ministers will be experienced MPs and peers it's often relatively simple to do this. However as Gulf Stream Blues has noted, the Mayoral administration has to recruit for the most part from outside the political mainstream and has very little time to do so. During the election Boris Johnson refused to list who would he appoint as he was the candidate standing not them, but it left little time to do the appointment checks.
The seemingly obvious solution would be to have a gap between the election and taking office. But this would mean the incumbent Mayor would remain in post for the time being, empowered to take decisions despite potentially having been rejected by the voters - not a good recipe for decisive decision making in a country not used to lame duck politicians. Just what is the solution here?