Ian Charlesworth, chief executive of the trust, was dismissed in August five days after warning trustees that the plans were too risky and could jeopardise the charity's finances (6 August, page 1).
Trustees have now decided not to proceed, blaming "the current UK situation" for the change of heart.
The news comes shortly after the resignation of Julie Currin, chief finance officer. Currin had also voiced concerns about Australia.
Management broke the news to employees in the weekly staff bulletin Shaw Thing on Monday.
"There are a number of reasons for this decision and these reasons are more to do with the current UK situation than the case for investment in Australia," it said.
"The decision was taken reluctantly as the reason for not entering the Australian market was one of timing rather than any question of the quality of the business case or the opportunities."
Catherine A'Bear, chief officer for corporate affairs, said she could not comment on the developments.
Charlesworth, 61, claims he was fulfilling his duty by alerting trustees to concerns about the Australia plans and is fighting to be reinstated. Chief executives body Acevo is supporting him.
He has also filed a grievance against director-general Tim Pape and chairman John Briffitt, claiming he was the victim of bullying, harassment and victimisation.
"Ian feels his warnings about Australia have been vindicated," a source at the Shaw Trust said.
Stephen Bubb, chief executive of Acevo, said: "The resignation of the finance director, on top of the summary dismissal of the chief executive, raises serious questions about the direction of the organisation. The Charity Commission needs to resolve this."
Commission officials met trustees this month to discuss concerns raised by Charlesworth about financial management and governance at the trust, which derives the majority of its income from the Department for Work and Pensions.