I was curious about this so googled for info, it seems that while BJ is getting the credit, Ronnie Flanagan had at least as much influence on the resignation:
"...on Wednesday Sir Ronnie called an urgent meeting of the Metropolitan Police Authority, the independent body which oversees the force, to brief its members on fresh allegations that Sir Ian had used Impact Plus to give him advice on his image when he took up his job.
No other company was invited to bid for the £15,000 contract it was claimed, even though Impact Plus had no specialist knowledge of public relations.
Sir Ronnie is understood to have discussed with the MPA the possibility of suspending Sir Ian, which would have made his position untenable.
Later on Wednesday Boris Johnson, the Mayor of London, held a meeting with Sir Ian at which he made it clear he had lost confidence in the Met chief and did not feel able to work with him. Mr Johnson, who chairs the MPA, may even have called for a vote of no confidence in Sir Ian at a meeting of the MPA next Monday.
It now appears that Sir Ian decided to quit before he had to face such humiliation.
Home Office sources have claimed Sir Ian displayed "very poor judgement" over the awarding of contracts to Impact Plus. "