Dacre is thought to have stepped in above John Teal, the advertising sales director, and Guy Zitter, the paper's managing director, to stop the Daily Mail running the ad.
The Daily Telegraph has also refused to run the ad which features caricatures of Prince Charles and Camilla Parker Bowles under the headline: "It's time to end the royal farce."
However, the ads are due to run in The Independent, The Guardian and The Scotsman on April 7, and the Daily Herald in Glasgow ran the ad earlier this week.
The move, which sees an editorial department intervene in its ad sales, is in contrast to the recent situation where adverse editorial saw Marks & Spencer pulling its ads from all Associated Newspapers titles.
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