Jacqui Lambie is set to pass the Coalition’s union penalty bill despite John Setka’s exit from the Labor party, after Anthony Albanese got his wish to remove the controversial unionist.

On Wednesday – two days ahead of a national executive meeting to push him out of the party – Setka tendered his resignation. He also abandoned an appeal he had filed to contest the process initiated by Albanese, who alleged Setka had brought Labor into disrepute.

Albanese declared the move a win for Labor values including respect for women, prompting Setka to issue a blistering statement attacking his leadership and attempting to link the decision to wider labour movement anger at Labor’s position on the Indonesian free-trade agreement.

A spokeswoman for Lambie confirmed to Guardian Australia that the senator’s position remains that if Setka does not resign as Victorian secretary of the Construction Forestry Mining Maritime and Energy Union she will vote for the ensuring integrity bill.

Given Centre Alliance’s Rex Patrick has said he will not support the bill in its current form and is seeking amendments, Lambie’s vote is critical to passing the bill which gives new powers to the federal court to make orders about the governance of unions and allows employers to request the deregistration or disqualification of union officials for breaches of industrial law.

Albanese told reporters in Canberra that Setka’s removal was important because it allowed Labor to demonstrate that “[its] values as a party are greater than any individual and that we’re prepared to stand up for those values”.

“I think that this is a good outcome for the Australian Labor party that allows us to draw the line under these issues and to confront a government that attacks workers’ rights, that doesn’t stand up for working values,” he said.

Albanese said Labor believed in the right to collectively bargain and to “deal with the power imbalance that’s there between individual workers and employers”.

“I will stand up for the rights of trade unions, but I’ll also lead a Labor party.”

In his statement, Setka said he “cannot continue to be a member of the Labor party while Anthony Albanese is its leader”.

Setka accused Albanese of attempting to push him out “based on false allegations [motivated] by old-fashioned political payback” after he decided his branch would stop financial contributions to Labor.

Setka accused Albanese of “turning his back on the values that underpin both the party and the union movement”, citing the fact he had abandoned Bill Shorten’s policy promises to “[stand] up for a progressive tax system, properly [fund] education and [abolish] the undemocratic, anti-union Australian Building and Construction Commission”.

“Just when I thought the Labor party couldn’t betray its principles and workers any further, it sided with the Morrison government on new free-trade deals with Indonesia, Hong Kong and Peru.”

Setka accused Labor of having “gone missing in action in the fight to stop the ensuring integrity bill”.

Albanese moved against Setka in June, citing comments denigrating the work of the anti-violence campaigner Rosie Batty – which Setka denies making – and later adding convictions for breaching a family violence intervention order and harassment as reasons for him to go.

The Australian Council of Trade Unions and many of its affiliates supported calls for Setka to resign but Setka refuses to leave his union position – a fact that will not change despite his exit from Labor, unless he is blasted out by his own members.

The attorney general and industrial relations minister, Christian Porter, called on Labor to go further and refuse the $1m of donations it takes from the CFMMEU while the Liberal senator James Paterson noted the union still controlled votes at Labor’s conference.