James, thank you for checking with the museum. I found another photo that's possibly the same car & driver, labelled as Ivy Cummings with her father Sydney. I think the date for both photos is 10th April 1920. The car is possibly a Grégoire special with the nickname "Perky".
https://gallica.bnf.fr/ark:/12148/btv1b530364606/f1.item.r=brooklands
https://gallica.bnf.fr/ark:/12148/btv1b53036492b.r=brooklands?rk=321890;0