The government’s signature tax policy will go to a vote in the Senate on Thursday.

The legislation will be sent back to the lower house after the Senate voted down part of the plan on Wednesday.

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But the government can simply use its numbers in the House of Representatives on Thursday morning to reject the changes and send its legislation straight back to the Senate.

A late decision by the Senate on Wednesday ensured there will be no more debate when the bill returns with an immediate vote required.

Earlier, the Senate voted to reject the controversial ‘third stage’ of the Coalition’s income tax cuts, which would have removed an entire tax bracket in 2024 so those earning between $41,000 and $200,000 were taxed at the same marginal rate.

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The Labor amendment was supported by the Greens, the Centre Alliance and independent Tim Storer.

The vote is a blow to the Turnbull government’s signature economic policy from the 2018 Budget, but the government can still reintroduce the package and try again.

“Of course we are committed to our comprehensive plan to deliver long-term personal income tax reform,” Prime Minister Malcolm Turnbull told reporters at Parliament House.

“This is a comprehensive plan that is founded on encouraging the aspiration and the enterprise of Australians.”

The government had been insisting on passing the three stages of its tax plan in one bill, forcing senators to vote on the 2018 cuts, which mostly benefit low and middle-income earners, while also locking in future cuts in 2022 and 2024 with more substantial benefits for higher earners.

But from the beginning, Labor and the crossbench wanted the bill split so each stage could be debated on its merits.

A further amendment to split off the 2022 cuts, which lift the ceiling on one of the middle tax brackets from $90,000 to $120,000, will be debated soon.

The bill will now head back to the House of Representatives, where the government can decide whether to reattempt the full bill.

One Nation is yet to finalise its policy on the cuts but appears to be leaning towards supporting the government.

One Nation Leader Pauline Hanson's support for the legislation has changed several times, previously indicating she would only support the earlier rounds.

But One Nation voted with the government to keep the package whole. Senator Brian Burston, who recently defected to Clive Palmer’s new party, supports the whole package.

Independent crossbencher Tim Storer blasted Centre Alliance senators for their siding with the government in guillotining debate.

"Centre Alliance turned its back on the principles central to Nick Xenophon and the party he started," Senator Storer said of his former colleagues.

"Senators Patrick and Griff stitched up a deal with the government to have their way, but deny others the chance to reduce the risks at the heart of the Government’s three stage tax package."