The Australian Council of Trade Unions (ACTU) has called on Tony Abbott to end the Royal Commission’s “political witch-hunt”, after fresh questions arose about the impartiality of its head.

Royal commissioner Dyson Heydon has agreed to give the ACTU until Thursday afternoon to formally decide whether to pursue his disqualification as head of the Royal Commission into Trade Union Governance, with any application to be heard on Friday.

ACTU secretary Dave Oliver said on Monday that documents provided to the Union showed Justice Heydon knew a conflict of interest existed in a Liberal Party event he had been asked to address.

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“Tony Abbott should be concerned the captain’s pick… that has now been seen to have genuine concern about bias, this is now up to Tony Abbott to fix this problem,” Mr Oliver said.

He called on Prime Minister Abbott to “shut down this political witch-hunt and stop wasting taxpayers money”.

The call comes after it was revealed by Fairfax Media that Justice Heydon had a personal connection with Mr Abbott going back decades.

The connection with Mr Abbott dates back to his selection as a Rhodes scholar in 1980, as a 23-year-old student at Sydney University.

Documents at the NSW state archives confirm a “Professor JD Heydon” was a member to the committee that selected Mr Abbott for the prestigious scholarship, that saw him attend Oxford University.

In a press conference discussing a new campaign against methamphetamine, Mr Abbott was questioned about the Rhodes link, but said he could not recall whether Mr Heydon was on the committee.

“That’s a long time ago and the idea that I gather is being peddled that somehow he and I cooked up a conspiracy 34 years ago against the Labor Party is absurd,” he said.

Justice Heydon provided a “no comment” response to questioning, according to The Age.

Meanwhile, the head of the Royal Commission into Trade Union Governance continues to face backlash after agreeing to speak at a Liberal Party event.

In a statement on Monday, he said he was approached last April to give the address at the sixth annual Sir Garfield Barwick Address in Sydney later this month.

“However, in March 2015 I overlooked the connection between the person or persons organising the event and the Liberal Party which had been stated in the email of 10 April of 2014,” he said.

When responding to the request last year, Justice Heydon said he would be “amenable” to giving the address if the commissions work had been concluded.

At that stage a final report was due in December 2014, however the timeline was later extended 12 months.

Justice Heydon said emails from April last year “did not state and I did not understand from it that the Sir Garfield Address was in any sense a fundraiser for the Liberal Party”.

The commissioner confirmed he could not attend the address last week, after it was revealed it was a fundraising event.

On Monday, lawyers for the ACTU successfully applied to have documents relating to Justice Heydon agreeing to appear at a Liberal Party fundraiser released.

They made the application to the Royal Commission into Trade Union Governance and Corruption.

The ACTU is now considering whether it will make a second application, which calls for the disqualification of the commissioner because of bias.