Have you tried the Public Record Office, Kew? You can check their online catalogue for the piece number for the ship at www.pro.gov.uk.
The passenger lists [BT 27] run from 1890 to 1960 and are arranged year by year under the port of departure. Details include the occupation, age of each passenger and usually the place of residence in the UK. I had a quick look and this may be correct [but please double-check]:
BT 27/1053 Port: Liverpool 1924 November(Part), December.
Sue