Murdoch’s resignation comes two months after he relinquished his role as News International executive chairman, following intense pressure to quit.

Murdoch, whose father is News Corp. chief executive Rupert Murdoch, is currently the deputy chief operating officer at News Corporation, which is BSkyB’s controlling shareholder with a 39 per cent stake.

BSkyB deputy chairman Nick Ferguson will step up as chairman, while Murdoch, who was appointed chairman in 2007, will stay on the board as a non-executive director.

The Shareholder lobby group Pensions & Investment Research Consultants said “the decision was inevitable”, but wants Murdoch to leave the BSkyB board entirely.

“In reality, the company should have appointed an independent chair last summer, to create a clear separation between the management of the business and the scandal at News Corp. Failure to act more quickly has resulted in self-inflicted reputational damage.”

Rupert praised his son for a “successful leadership”, while Murdoch said in his own statement: “I am aware that my role as chairman could become a lightning rod for BSkyB and I believe that my resignation will help to ensure that there is no false conflation with events at a separate organisation.”

In just a few weeks a parliamentary report is due into reporting practices at News of the World.