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The Ballarat left from Gravesend for Sydney on 17 June 1926
(reported Friday, June 18, 1926
Publication: The Daily Telegraph)
It arrived in Table Bay on 9 July 1926
(reported Tuesday, July 13, 1926
Publication: The Daily Telegraph)
It arrived Fremantle on 26 July 1926
(reported Wednesday, July 28, 1926
Publication: The Daily Telegraph)
It arrived Adelaide on 2 August 1926
(reported Thursday, Aug. 5, 1926
Publication: The Daily Telegraph)
Arrived Melbourne 6 August 1926
https://trove.nla.gov.au/newspaper/article/3800278and finally arrived Sydney on 11 August 1926
(reported Friday, Aug. 13, 1926
Publication: Aberdeen Journal )
It's quite likely he went under the Empire Settlement Act. Not sure how much it would have cost. On the return journey the fare on the Ballarat was advertised as £37-£45 single from Sydney to London.
https://trove.nla.gov.au/newspaper/article/246355208A picture and some details of arrival here:
https://trove.nla.gov.au/newspaper/article/239854565https://trove.nla.gov.au/newspaper/article/222718927https://trove.nla.gov.au/newspaper/article/16321551https://trove.nla.gov.au/newspaper/article/246350362Various other mentions if you search trove:
https://trove.nla.gov.autrove is also an excellent source you could use to find out more about his life in Australia.