The show, running at the St James’s gallery from May 30 to July 8, is held to mark the Platinum Jubilee and showcases royal commissions which the firm has organised.
Philipps has completed other royal depictions, notably the 2010 double portrait of princes William and Harry which is in the National Portrait Gallery and another portrait of the queen, first commissioned by Royal Mail for a first-class stamp, which is now on display as part of the Royal Collection.
This oil on canvas, 6ft 8in x 3ft 4in (2.03 x 1.01m), is offered for a price in the region of seven figures.