If have looked at the right people.

Her Father was a William James TERRILL, bap 15 Jun 1870 in Devonport, DOB given as 31 May 1870.

There is a William J TERRILL on the 1939 Register in Sheerness, Kent with DOB of 31 May 1870, Occupation given as Sanitary Inspector. This would tie up with job of Health Inspector as given on Dorothy's Marriage Certificate.

Only thing is he is given as married to a Minnie not to Jessie, but could be a 2nd wife, if Jessie died abroad and William remarried.

Believe that this William died 4 Jan 1948 in Southall, Middlesex as there is an Administration granted to a Minnie Emma Theresa TERRILL on the 18th March 1948. Unfortunately as only an Admin will be no will so not possible to know for certain if is the William TERRILL father of Dorothy