Theresa May is under mounting pressure to ditch a fresh immigration clampdown dubbed “the next Windrush”, ahead of a crucial Commons vote next week.

Thirty-four organisations have joined forces to urge the prime minister not to repeat the blunders that sparked the scandal by preventing other immigrants from proving their right to be in the UK.

Under planned new data laws, people will be denied access to the personal information the government holds about them if releasing it would “undermine immigration control”.

Leading lawyers have warned that withholding potentially vital proof would lead to people being wrongly deported, detained or denied health treatment – in a mirror image of the treatment of the Windrush generation.

On Wednesday, Labour and the Liberal Democrats will join forces to try to throw out the exemption, arguing it is the “first test” of Ms May’s promise to learn the lessons of the Windrush debacle.

Now, the joint letter – seen by The Independent – brings together human rights campaigners, trade unions, migrant support groups and law firms to warn it will “foster fear within minority communities”.

Unless halted, the plan will make it “near-impossible” to prevent the “disposing of information that could help people prove their right to reside in the UK – as it did with the Windrush landing cards”, they say.

People would also avoid using essential public services “for fear that their medical or school records will be secretly passed to the Home Office”.

Martha Spurrier, the director of Liberty, which coordinated the letter, said: “This exemption is discriminatory, unjustified and will make it near impossible for immigrants to legally secure their status. It must be removed now.”

Lucy Jones, of Doctors of the World, which works closely with undocumented migrants, said: “We regularly see patients, often in urgent need of medical care, who are too afraid to go to NHS services fearing their information will be shared across government. The exemption makes this fear an absolute reality.”

And Adrian Berry, chairman of the Immigration Law Practitioners’ Association, highlighted how lawyers for migrants would no longer be able to obtain their files using “subject access requests”.

“The impact the exemption will have on curtailing access to personal data therefore goes to the very heart of access to justice and the preservation of the rule of law,” he warned.

Amnesty, the Refugee Council, the National Aids Trust, the National Education Union, Privacy International and the trade union Unison are among the other organisations which have signed the letter, sent to Sajid Javid, the new home secretary.

The Independent revealed last October that the exemption in the data protection bill would remove data privacy rights for immigration investigations.

However, the controversy has grown in the wake of the Windrush scandal – prompting the crucial amendment, put down by Labour and the Lib Dems, to be debated on Wednesday.

The prime minister was accused of being in denial about the issue, when she told MPs recently: “It will be possible for people to access the information that they need.”

In reality, the bill clearly states the rights to personal data “do not apply” where that conflicts with “the maintenance of effective immigration control” or “the investigation” of suspected immigration offences.

Ed Davey, the Lib Dem home affairs spokesman, told The Independent: “This is completely against the British traditions of justice and the rule of law. It is an odious proposal.

“If Theresa May doesn’t change her mind on this, no one will be able to take seriously a word she has said since Windrush. This is the first test.”

The Home Office made “a lot of mistakes”, Mr Davey said – sometimes trying to deport “completely the wrong person” – which were only thwarted by the right to open up files.

Tom Watson, Labour’s deputy leader, said the policy was a “continuation of the government’s hostile environment policy”, adding: “Given the government’s track record in this area there no guarantee that it would exercise any exemption properly or proportionately.

“Labour will support measures to delete this exemption from the bill when it returns to the Commons next week.”

The Home Office has insisted the right to request data “will be met in all cases except where to do so could undermine our immigration control”.

A spokesperson said: “They will have the right to complain to the information commissioner if they disagree with any use of the immigration exemption and we would always want to assist those whose claims are in question.”

However, lawyers have rejected that right to appeal, warning a person would probably have been deported before a ruling came through.

After his appointment last week, Mr Javid dropped the use of the “hostile environment” phrase – favoured by the prime minister – but has yet to say he will change the policies behind it.