Unfortunately, incoming passenger lists only survive for voyages originating outside Europe / the Mediterranean: https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/passengers. 

A small number of aliens' registration cards have survived for the period 1918-1957: https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/aliens-registration-cards-1918-1957. There are also records of enemy aliens who were interned: https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/internees (unlikely to apply in your father's case).

Naturalisation would have been required for a British passport. Records are available up until 1986: https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/naturalisation-british-citizenship.

Caroline Gurney
Bristol, UK