Tony Abbott's government is embroiled in a new political crisis just weeks after the Bronwyn Bishop affair, with the Prime Minister digging in on Thursday against calls to dismiss his hand-picked head of the royal commission on trade union corruption, Dyson Heydon, for perceived political bias.

The opposition mounted a full-throated attack in Parliament, including an unsuccessful censure motion over the former High Court judge's links to the Liberal Party, after Fairfax Media revealed exclusively that he was to address a Liberal Party event as its guest speaker later this month.

A flyer for the speech stated that any funds raised from the address would support Liberal Party state campaigns.

The revelation that a serving royal commissioner had agreed to give the Liberal Party's annual Sir Garfield Barwick Address at Sydney's Castlereagh Boutique Hotel sent shockwaves through the government, and saw Mr Heydon pull out of the event on Thursday morning, claiming he had not known of its status as a potential fundraiser.

In full damage-control mode on Thursday, the Liberal Party has since claimed the $80-seat dinner would have raised very little.

However, the story has raised fresh questions over the government's decision to appoint the eminent jurist - known for his conservative views - and called into doubt the propriety of retaining him in a role that deals with bitterly contested issues and has already seen him clash with Labor leader Bill Shorten during proceedings.

Labor argues the whole royal commission, which it has always regarded as a witch-hunt, has been exposed for the political exercise it is. Its manager of business, Tony Burke, demanded in Parliament that Mr Heydon be dismissed.

"This is conflicted, he is biased, the royal commission is a farce," he said.

As the government struggled to defend itself, Mr Abbott contradicted himself over whether the event was or was not a Liberal Party fundraiser, giving two different definitions in Parliament.

Elsewhere in the Senate, Attorney-General George Brandis was also on a different track, claiming it had not been a party political event at all.

Yet Mr Brandis had himself given the same address in 2010, and had claimed more than $1000 in travel entitlement to do so.

Defending Mr Heydon in Parliament, Mr Brandis denied it was a political event, and denied that his planned attendance in any way called into question the commissioner's impartiality.

"I am aware that the royal commissioner, Mr Heydon, was scheduled to deliver the Garfield Barwick address at a function arranged by the New South Wales Legal Practitioners Branch of the Liberal Party," he said. "That function is a public function; it is not a political function."

However, Labor described that explanation as nonsense.

Among the factors weighing against Mr Heydon's continued role are his own words in the case of British American Tobacco Australia Services Limited v Laurie, in which he addressed specifically, the importance of appearing to be fair.

"It is fundamental to the administration of justice that the judge be neutral," he had written.

"It is for this reason that the appearance of departure from neutrality is a ground of disqualification … because the rule is concerned with the appearance of bias, and not the actuality, it is the perception of the hypothetical observer that provides the yardstick."

In an endeavour to establish that he had pulled out of the event prior to being contacted by Fairfax Media, Mr Heydon released two emails between his office and the event organiser, Gregory Burton.

However, the emails do not show, as claimed by the government, that he had pulled out. Rather his reply to what is suspected as being a Liberal Party branded email (sections have been redacted) from Mr Burton, dated the day before, shows Mr Heydon's assistant had stated that he would be coming, although with certain conditions. These were that he would not be accompanied, would not answer questions afterwards and, importantly, would not attend at all if the event were capable of being described as a Liberal Party event.

The government argued this proved he was not engaging in a political function.

But Labor said he had known of the event's status as Liberal Party event since agreeing to do it in April, and that he was well connected to it because his counsel assisting in the royal commission, Jeremy Stoljar, SC, was in regular contact with Mr Burton.

Mr Burton, who has himself donated thousands to the Liberal Party in the past, has been discussed as a possible replacement for Bronwyn Bishop in the event of her retirement from the safe Liberal seat of Mackellar.

Speaking at a media conference shortly after question time, shadow attorney-general Mark Dreyfus called on Mr Heydon to release all communications between himself and the Liberal Party.

Greens MP Adam Bandt also said the royal commission must be terminated.

"Any pretence of independence of the trade union royal commission is now gone," he said. "And the royal commission must be immediately terminated."

A bio accompanying a photograph of Mr Heydon on the flyer for the address does not disclose he is serving as royal commissioner.

Prime Minister Tony Abbott vowed to establish the royal commission in the wake of the Australian Workers Union slush fund scandal, which dogged former prime minister Julia Gillard.

It was also established to examine the corruption uncovered at the Health Services Union involving former Labor MP Craig Thomson.

In selecting Mr Heydon to head up the royal commission, Mr Abbott said in July: "There is no more distinguished person in the legal profession than Justice Dyson Heydon."

The opposition has condemned the royal commission as a political witch-hunt and stepped up its criticism after Mr Shorten was called to give evidence relating to deals he struck for workers as head of the AWU.

The invitation for Justice Heydon's address was first posted in April, three months before Mr Shorten's appearance.

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