Milburn was appointed the chancellor of the Duchy of Lancaster in Tony Blair's reshuffle last week, a position previously held by Douglas Alexander, who was also the cabinet minister in charge of COI Communications.
Although the cabinet office has not yet published its new list of ministerial duties, Milburn's deputy, Ruth Kelly, will take over the COI brief.
Officially, the government will argue Milburn will be too busy overseeing the development of policy to take on other posts. But sources admitted he would have faced allegations of a conflict of interest if he had been responsible for Whitehall advertising in the run-up to the general election expected next May.
Kelly, the new cabinet office minister, will hold talks shortly with Alan Bishop, COI's chief executive. Under him, COI's performance has impressed the cabinet office.
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