The painting, Maternal Affection, is an oil on copper work from 1773 by Louis-Jean-Fraçois Lagrenée.
Sewell, who died in 2015, acquired the painting in the 1960s. It is one of a number of Old Master and British pictures in his collection, many of which were auctioned off at Christie’s earlier this year in a sale that totalled of £3.74m.
It is one of only 11 paintings by Lagrenée in the UK and the first in the National Gallery’s collection. It is hung in the London museum’s Room 33.
“I’m leaving my body to science," Sewell told the Mail on Sunday in 2014. "If there’s anything left, they can burn it, mix the ashes with bird food and scatter them on the steps of the National Gallery”.