yes, you are right, its an Australian Morris Major series II, made from 1959 to 1964, sharing the same basic body structure and engine as the Wolesley 1500 and Riley 1.5
All the car seems a mix of BMC-made parts...e.g.,headlight pods recall same shape of 1959 Austin A 40"'Farina" and grille shape resembles that of 1959 Standard Vanguard Vignale or Pennant