I'm no further along with this one, although I have just found a probate record for Frank's widow Mary Helena using
https://probatesearch.service.gov.uk/Calendar which confirms what we already know about her and the eldest daughter.
STAINTHORP Mary Helena of 10 Richmond Bridge Mansions Twickenham Middlesex died 18 May 1967 at West Middlesex Hospital Isleworth Middlesex Administration London 9 June to Margaret Irene Primrose Godfrey widow £831.
N.B. no will though
It's occurred to me that the younger daughter (Mary [He?]Lena "Mollie" Stainthorp) may have been placed into adoption - formally or otherwise - at the end of the War. She would have been five when her father died. That might explain the lack of any subsequent records. I'm going to take a punt and order the marriage and death certs for Mary Lena MILLS b.31 Mar 1913, m.1942 JURY, d.1973 to see if there are any clues that she was Mollie Stainthorp.
Alternatively it's possible that she emigrated, married MILLS overseas, and returned to marry JURY.
When the 1921 census and/or the 1939 registration records are released, perhaps I'll be able to tell whether the younger daughter was still with her mother and sister or at least still in England.