Traditionally thought to be that of Sir Thomas Browne by William Dobson. If you look at the picture of Thomas and his wife Dorothy painted by John Souch, there is a resemblance, so there is some reason to think this is John and his family, but no conclusive proof. He could have been in Oxford at the same time as Dobson, though as he was native to Norwich, would he have transported a young family across war torn England to Oxford to have a portrait painted?
Anyway, this is a lovely family group and their clothes put them firmly in the 1640s. They all look unerringly at the viewer, daring us to stare back. John (or whoever) is wearing a brown, (or what most people would have thought of as black) coat with a plain falling band and a simple black day cap. His wife is wearing a smart wide brimmed hat and what looks like a cream bodice under a dark mantle or wrap. The children are all in petticoats, though I suspect that the two on the right hand side are boys wearing red petticoats with linen aprons, bands and matching caps. The boy on the left has a small sword suspended from a blue ribbon, whilst the lad on the right is more interested in his pet rabbit. The two girls on the right, (they look old enough to have been breeched were they boys) are wearing russet coloured waistcoats with plain linen kerchiefs and black hoods over their coifs possibly indicating that they have lost siblings. John Browne lost several children at an early age (five out of eleven) so that fits with the Thomas Browne theory, though losing small children was by no means unusual.
Thanks to Chatsworth for permission to post this image. The painting is © Devonshire Collection Chatsworth and reproduced by permission of Chatsworth Settlement Trustees.