No replacement will be named until the fate of the Bates network, reeling from a series of devastating account losses, has been resolved.
Cracknell is switching to a part-time role working on strategic issues with Toby Hoare, who runs the Bates European operation. He will also seek non-competitive work outside the agency.
Aris Theophilakis, the newly appointed creative director for Bates Europe, would be an obvious successor. But Hoare admitted: "It's very difficult to make that happen at the moment."
Cracknell, 56, said: "I think it's time to move on. The job needs a younger man, someone who is not inhibited in their enthusiasm."
His exit comes as Cordiant fights for survival after Allied Domecq's decision to relieve it of £18 million worth of business. The brand assignments, which include Ballantine's whisky, Tia Maria, Tia Lusso and Malibu, are expected to be consolidated into Publicis, the drinks giant's other agency network.
The announcement plunged Cordiant into immediate crisis, casting doubt over its ability to publish its preliminary results and threatening the suspension of its shares.
The group, with debts of £250 million, confirmed it had received some preliminary approaches about a takeover, and described talks with its bankers as "constructive".
However, the prospect of the group surviving intact is looking increasingly slim. WPP and Publicis Groupe, the most likely parties willing to do business, are thought to be interested only in selected parts of the business.
David Bezem, a managing director at Close Brothers, the corporate financier, said: "Why would anybody want to take on Cordiant's debt when it's easier just to pick off the clients and the people you want? I fear we may be about to see the first major crash in the communications sector."
A notable prize for predators would be 141, Cordiant's integrated marketing specialist, which has 1,500 people operating in 91 countries and British American Tobacco as a major client.
Colin Hearn, 141's chief executive, said: "I intend to do everything I can to keep us together."
Cordiant is already believed to have begun talks with Publicis about the sale of its 25 per cent stake in ZenithOptimedia to the French group. Publicis has a right to buy at a pre-set price of £75 million, but can be expected to use Cordiant's plight to drive a hard bargain.
Meanwhile, Bates UK, already facing the loss of its Royal Mail and Woolworths accounts, is attempting to tie down its remaining business, including Sky TV and B&Q.