DCK, you’re right in thinking it’s the young lady’s telephone number: FRObisher 0409, which would have been somwhere in west London.
The UK went over to all-figure numbers in the late 1960s, and the number would now be 0207 370 0409.
Ah!
So she was living in the west of London. Must have been someone he met between 40 and 44 then.
Almost impossible to track her or her relatives down with only a last name from 1944.