You are quite right that the absence of a named father on the birth certificate of an intestate whose parents did not marry will lead to the father (and any person related through him) being regarded as having predeceased the intestate child.
This is however a presumption and so may be rebutted. Very unlikely it would seem for a war baby.
If rebutted however, then next in line to benefit would be the father himself and if not any half-siblings by the father. Thereafter then lines through both paternal and maternal uncles and aunts would come into play.
Missing beneficiary indemnity insurance would likely prove the most convenient safeguard for the personal representatives and any insurer would specify their requirements.