The Scurra was written by James Steen, the former Punch editor, and Dominic Midgely and is being dropped because it is thought to be too London-biased for the paper's traditional core readers in the North.
The column, which failed to appear in the newspaper yesterday, was written independently from an office in Battersea, south London.
Hitchens, the controversial former leftist who backed George Bush's policy in Iraq, is also losing his column. Wallace is reported to have said it was looking tired.
The move comes just weeks after regular columnists Matthew Norman and Jonathan Freedland lost their columns. Both were hired by Morgan in an attempt to take the paper upmarket.
Wallace has already enlisted former Loaded staffer Bill Borrows to replace Freedman. A northerner, he is thought to be more familiar to the paper's average reader. In a move to attract young women, Wallace has enlisted the help of Heat contributor Polly Hudson to front a weekly TV column with Nicola Methven, the TV editor.
Wallace's hiring was widely welcomed in the industry. After his appointment, Max Clifford, the PR guru, was reported to have said: "The big stories are what sell newspapers and he understands the Mirror philosophy. He knows what stories and celebrities are of interest to Mirror readers."
The Mirror confirmed the changes but declined to comment.
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