Just watched it this morning too! Caronia makes an appearance docked where the current Ocean Terminal is, Orcades being docked at the old Art Deco style (but built after WW2) Ocean Terminal. I also spied what seemed to be RMS Andes in the distance in one of the shots and what might be an older (at the time) Elders & Fifes Banana boat in the foreground of the same shot. The complete merger of Orient Line into P&O took place in 1966 which also dates the film.
I can also recommend "The Way Of A Ship" filmed on her sister Oronsay when new in 1953. The film also features the tug/tender Calshot assisting Oronsay in Southampton with a host of other tugs. Calshot being the last ship still afloat in Southampton that was present in the old days.