Following on from all those great ideas posted by other RChatters :
Yes, the Great War certainly curtailed civil voyages to and from UK – threat of being sunk by enemy was not the only issue – ships were needed to transport AIF and NZEF troops, horses and supplies from Australia and New Zealand to the front. And, the ships needed to be converted from carrying civilian passengers.
May I suggest : try manipulating the database at naa.gov.au ….
http://naa.gov.au/collection/search/ (Record Search, then to Passenger arrivals) So at passenger arrivals, enter ‘1915’ for year of arrival and ‘London’ for Port of embarkation, and nothing else ... I think this may be useful as it gives names of ships (click on the heading ship/aircraft name) and then you can seek out info about other voyages around the same time as your Osterley arriving Fremantle 23 December 1915.
So, from my armchair, I can see the following:
Medina, 1 Feb 1916
Star of England, 23 Jan 1916
Karmala, 5 Jan 1916
Osterley, 23 Dec 1915Maloja, 6 Dec 1915
Aeneas, 30 Nov 1915
Omrah, 27 Nov 1915
Mooltan, 20 Nov 1915
Kanowna, 14 Nov 1915
Malwa, 5 Nov 1915
I have not looked further, as I assume you have your own reliable resources at hand, and of course you would go through Trove for any cuttings and shipping news for those vessels. Likely you are familiar with Nicholson’s Log of Logs
https://catalogue.nla.gov.au/Record/1458167 Fingers crossed
JM