The company has appointed the City grandee Lord Jacob Rothschild as a non-executive deputy chairman, and sent two other non-executive directors, Allan Leighton and Gail Rebuck, to meet with key shareholders including the National Association of Pension Funds and the Association of British Insurers.
Murdoch's appointment as a replacement for Tony Ball has concerned many shareholders who believe it goes against best corporate practice - his father, Rupert Murdoch, is the chairman of BSkyB.
There was also anger that he was perceived to have been gifted the job because of his family connections and not because he was the best person to do the job. Rupert Murdoch's News Corporation owns 35.4 per cent of BSkyB.
However, the appointment of Lord Rothschild is intended to calm shareholder disquiet over BSkyB's corporate governance record and Murdoch Junior has embarked on a City charm offensive to prove he is equipped to do the job.
Recent events in the City have shown that shareholders are prepared to be ruthless if they feel their views have been ignored. Investor power proved to be the downfall of the Carlton chief executive and ITV plc chairman designate, Michael Green, last month and observers think that the chairman of BSkyB's nomination committee, Lord St John, could be the target of investor unrest at BSkyB's annual meeting next week.