“That is obviously open to the CFMEU to undertake that legal challenge and again this is one of the reasons that we wanted to get this legislation passed quickly,so that we can move through as many stages as possible,” he said in Canberra.

Opposition workplace relations spokeswoman Michaelia Cash conceded the letter from Irving on donations was not legally binding but said she was prepared to accept his assurance.

“I have accepted what minister Watt has provided to me,if this is indeed not true,then that is a reflection on minister Watt,” she said.

Greens leader Adam Bandt criticised the major parties’ agreement. “Labor and the Liberals have just cut a deal to ram through flawed and draconian laws that threaten fundamental rights,” he said in a statement. “Civil liberties groups have rightly said this bill is a threat to freedom of association and the rights of all unions and membership-based organisations.”

Opposition Leader Peter Dutton’s move to table a bill to bring back the union watchdog scrapped by Labor,the Australian Building and Construction Commission,and another allowing lifetime bans for corrupt union officials was knocked back by Watt,who said it would be “a witch hunt against all unions”.

Earlier on Monday,Senator Jacqui Lambie used parliamentary privilege to accuse major contractors of working with the CFMEU to engage in price fixing on government projects and allege that construction workers were being forced to join the union to work on them.

“I have a very good source that construction workers are being compelled to join the CFMEU for an annual fee of $1200 as a condition for participating in Victorian Big Build projects,” she said. “This practice raises serious concerns about the violation of workers’ rights and the enforcement of freedom of association,which is a fundamental legal principle in Australia.”

Lambie said she was told this practice was happening on worksites run by “foreign-owned” tier 1 contractors.

“I have also received credible information that suggests that these tier 1 contractors may be colluding with the CFMEU to breach anti-competition laws and engage in price fixing on government projects,” Lambie said. “This alleged conspiracy involves selecting only CFMEU endorsed non-competitive labour hire firms undermining fair competition.”

Lambie called on the government to withhold money from projects if contractors continued to “turn a blind eye” to corruption on sites.

Speaking in the Senate,she called on the government to investigate revoking Australian work rights for Gerry McCrudden,citing reports in this masthead that the high-ranking CFMEU official warned that any firms without the union’s backing would be unofficially black-banned from all Victorian Big Build sites.

Also in the Senate,Lambie named Victorian branch senior vice president Joe Myles,saying she understood he played a “significant role in organising these activities”.

Myles did not respond to a request for comment and nor did the CFMEU’s national office. McCrudden could not be contacted.

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