Rebellious ministers believe Theresa May will be forced to allow workers earning at least £21,000 to enter the UK after Brexit in the face of intense lobbying from businesses demanding the right to employ low-skilled workers from abroad.

The prime minister had wanted to limit the vast majority of immigration to people with jobs paid £30,000 and over, but had already had to concede there would be a further year of consultation on the threshold after a cabinet revolt.

And within hours of the publication of the government’s long-awaited immigration white paper on Wednesday, uproar from business groups over the proposals deepened the cracks in what had been intended as one of the flagship policies for May’s vision of post-Brexit Britain.

Philip Hammond, the chancellor, and Greg Clark, business secretary, who led the revolt, now expect employers’ groups to lobby hard to slash the prime minister’s preferred £30,000 threshold.

The white paper sets out how free movement from the EU will end after 2021. Free movement is widely regarded as one of the key reasons for the Brexit vote.

The document proposes a skills-based system that makes no distinction between EU and non-EU countries, but the cabinet standoff meant that no final decision on the all-important salary threshold could be reached.

Sajid Javid, the home secretary, presenting the white paper, told the Commons that the original £30,000 level proposed by the independent Migration Advisory Committee was “not set in stone”.

Conceding that ministers needed to do further work, Javid added: “We will have to have more engagement to ensure that we get it right and come up with a threshold that we believe works for all parts of the UK.”

One cabinet source said that given the pressure from employers they expected the final outcome “to be likely to be closer to £21,000 than £30,000”. Allies of Hammond said he was “very content” with the outcome and looked forward to the consultation taking its course.

Home Office officials also refused to predict whether the new regime would reduce immigration, saying that future migration levels would depend on a range of factors that were hard to predict.

That reticence echoed Javid’s own refusal to repeat May’s 2017 election manifesto pledge to bring net migration down to “tens of thousands” in a morning radio interview on the BBC.

When asked directly if the target of “tens of thousands” had been abandoned, Javid would only say: “What was clear from the manifesto was our commitment to bring net migration down.”

The goal of cutting net migration – the difference between the annual number of people arriving in the UK versus the number leaving – was set by David Cameron’s coalition government in 2010. The target has never been met, with annual net migration standing at about 244,000.

The white paper itself refers indirectly to May’s long-held target. It said the government is still committed to “reduce annual net migration to sustainable levels as set out in the Conservative party manifesto”.

Downing Street has been trying to get the immigration white paper published for a year, believing that the introduction of strict border controls is a trump card at a time when May is struggling to persuade rebellious MPs to sign off on her Brexit deal reached with the EU.

Insiders believe publishing the document remains an important achievement given how contentious the subject has been within government. No 10 sources also argued that the prime minister was following the advisory committee recommendation, which had originally floated the £30,000 figure.

Business organisations immediately began the next phase of lobbying, voicing concerns about the effect of the £30,000 salary threshold on the British economy, which has sucked in lower-paid workers from the EU in the past two decades.

Josh Hardie, the deputy director of the CBI, said: “Hospitals, housebuilders and retailers are all struggling to find the people they need at salaries well below £30,000. These proposals must change.”

Mike Cherry, the chairman of the Federation of Small Businesses (FSB), warned that seven in 10 small employers relied on mid- or low-skilled staff who could be disqualified from working in Britain if the £30,000 limit was used.

“Getting this threshold wrong will cause serious disruption to the economy. With the employment rate at a record high, small firms are already struggling to access the skills they need,” said Cherry.

Sectors such as construction and social care, where low pay predominates and employers have become particularly reliant on EU workers, are among those highlighted as likely to be affected.

Brian Berry, the chief executive of the Federation of Master Builders, which represents construction firms, complained about the “obsession with salary thresholds” and said the £30,000 figure “was met by fierce opposition from almost all sectors” when it was floated by the advisory committee.

No 10 had tried and failed to head off the political and business revolt with a pledge to introduce a temporary low-skilled workers scheme, as an insurance policy for the most affected sectors.

The transition measure, to be introduced for five years, will allow people with lower-paid jobs to come to the UK for a maximum of 12 months, with a cooling-off period of a further 12 months to prevent people settling in the UK as a result.

The new immigration rules are due to be come into force at the end of the post-Brexit transition period, at the beginning of 2021. The long consultation means businesses could have no more than a year to adapt once the threshold is set.

An additional “small-scale” scheme for fruit pickers and other seasonal agricultural workers will be trialled in 2019, but no other specific sectors of the economy will be allowed special treatment, the white paper says.