Instead, the Government fielded John Denham, a junior minister, to answer questions about the review of disability and sickness benefits.
Last week, in a leaked exchange of correspondence between David Hill, Labour's director of communications, and Jon Barton, editor of the Today programme, Mr Hill disclosed that the party had held a "council of war" over the treatment meted out to Ms Harman by John Humphrys.
Mr Hill warned that if interviewers continued to interrupt ministers, blocking out the message, they faced the risk of the party refusing to supply ministers to the programme.
Yesterday, the row grew when James Cox, presenter of The World this Weekend, said Labour had "apparently withdrawn co-operation from us because Ms Harman declined to come in to talk to me".
But Mr Hill protested: "They know that that assertion is ridiculous. The question of which social security minister goes on their programme is a matter for the department, not the Labour Party, and The World This Weekend know it ... The Labour Party will be forced by this action to exercise rigid demarcation so that we can only assist the BBC with bids which are strictly party political. That is the inevitable outcome if the BBC persist in acting in this way."
A spokesman for The World This Weekend said Mr Cox's remark had been intended as "light-hearted" and was "not meant to be taken seriously".