Campaigners against the UK’s controversial drug pricing deal with Donald Trump are threatening the government with legal action unless it scraps a key element of the plan.

They claim that a change to how drug treatments are approved for use by the NHS, which could lead to it paying even higher prices for them, amounts to an “unlawful power grab”.

The plan could let the health secretary override the independent judgment by the National Institute for Health and Care Excellence (Nice) as to how much the NHS should pay for certain medicines.

Campaign groups Global Justice Now and Just Treatment have warned the Department of Health and Social Care (DHSC) that they may seek a judicial review in the high court of the legality of such a move.

They told the department they would press ahead with seeking a judicial review unless it revoked the statutory instrument – secondary legislation – which came into force last month, giving ministers the power to overrule Nice. The institute is respected worldwide for its independence from ministerial control.

The loss of Nice’s longstanding independence as the body that decides which drugs the NHS in England and Wales should buy is part of the government’s medicines agreement with the Trump administration which was announced last December.

Nick Dearden, the director of Global Justice Now, said: “This is a government gambling with NHS patients’ lives in a geopolitical game with Donald Trump.

“They risk sabotaging our carefully worked-out mechanism for keeping a lid on big pharma’s overinflated prices, and they have done so without so much as a debate in parliament.”

Lawyers Leigh Day have sent the DHSC a nine-page “letter before claim” on behalf of the group and Just Treatment. The Conservative former health secretary Andrew Lansley has said the statutory instrument is unlawful because it clashes with the Health and Social Care Act 2012.

MPs from several parties, including Labour, have voiced concern about the secrecy surrounding the deal and the government’s refusal to release its impact assessment of the long-term cost of the decade-long deal with the White House, give any detail in replies to parliamentary questions or allow a debate about it in the Commons.

Diarmaid McDonald, the director of Just Treatment, said: “They’ve refused to publish their own assessments of the damage the deal will do to the NHS and they’ve used a parliamentary process designed to make it extremely difficult for MPs to properly scrutinise what they are up to.

“But we believe the process they have followed is unlawful and we are ready to take them to court to defend NHS patients and our democracy.”

The Guardian reported last month how dozens of MPs from a range of parties had shown their concern at the potential end to Nice’s independence – and that Lansley believes the government is breaking the law.

Ministers said the deal will mean more NHS patients get access to innovative medicines. It will ensure that UK drug exports to the US remain tariff-free for three years.

The spokesperson for the DHSC denied that the change overrides Nice’s independence.

“Nice’s independence will always be protected. It will continue to set out guidance and make recommendations entirely free from political interference, balancing clinical effectiveness with making sure taxpayers get a good deal,” they said.

“There is a revolution taking place in medical science, and we are determined for this to benefit patients, making it easier to bring innovative medicines to the NHS.

“This will mean thousands of patients have access to life-changing new treatments, including recently approving a brain cancer drug for patients as young as 12.”

A DHSC source added: “Nice’s legal framework states that ministers are not able to direct Nice as to the substance of its recommendations.

“Nice remains responsible for independently deciding whether a medicine can be recommended as a clinically and cost-effective use of NHS resources.”