Burke, who has been in the position for just five months, took over in February this year following the departure of John Lovering.
In that time he has seen M&B's food sales overtake that of drink for the first time, and overseen a move for the group into developing a possible pan-Asian food concept with the appointment of former Tampopo executive chef Adrian McCormack.
But Lovering himself had been in the role for just one year, having taken over from Simon Laffin after a bitter shareholder dispute in January 2010.
Burke’s departure has caused speculation that all has not settled at M&B following a series of management shakeups that has also seen the departure of chief executive Adam Fowle in March this year.
In addition, Michael Balfour, non-executive director of M&B, has also decided to step down.
The Board has appointed non-executive director Bob Ivell, who joined the company in May this year, as non-executive chairman for the time being.
Ron Robson, a non-executive director on the board since January 2010, has been appointed the role of deputy chairman.
M&B still expect to release an interim management statement later this month as scheduled.