Plans drawn up by Boris Johnson’s government to remove senior civil servants from key ministries has resulted in a “poisonous” atmosphere across Whitehall, according to union leaders.

Amid reports that the prime minister is targeting three permanent secretaries who have previously offered unwanted advice, the FDA and Prospect unions said unattributable briefings from No 10 had damaged the government’s machinery.

It has followed a series of threats by Dominic Cummings to radically shake up Whitehall, as well as the high-profile sacking of a special adviser, or Spad, who is taking No 10 to an employment tribunal.

The home secretary, Priti Patel, had last week sought to oust her most senior civil servant, Sir Philip Rutnam, government sources have confirmed. The Sunday Telegraph reported that the prime minister’s aide would also like to remove Sir Tom Scholar from the Treasury and Sir Simon McDonald from the Foreign Office.

Dave Penman, the general secretary of the FDA union, which represents permanent secretaries, said the suggestion of a hit list of senior civil servants is a “self-destructive low” for No 10.

“These cowardly briefings against officials – who they know are not allowed to answer back – do untold damage to the trust between civil servants and ministers, far wider than the ministries targeted in this round of back-stabbing.

“Civil servants will wonder what kind of organisation so publicly undermines its most senior and able staff for a quick headline, and potential candidates will wonder whether it’s the sort of workplace they want risk their reputation in,” he said.

Johnson is said to want to remove Scholar for being “offside” on Brexit and the economy. McDonald worked alongside Johnson at the Foreign Office.

Garry Graham, Prospect’s deputy general secretary, said civil servants cannot offer honest advice if they are under constant threat. “Policy advice to ministers from civil servants needs to be empirically based and evidence-led – not based on whether they are a ‘true believer’ or not,” he said.

Johnson could struggle to remove any senior civil servants viewed as an obstruction because of a Tory plan to enforce a £95,000 cap on public sector payoffs, Whitehall sources told the Guardian.

Under previous governments, senior civil servants were often quietly paid off if there was a personality clash. But this route has been obstructed by plans to stop “golden goodbyes”.

The policy was put forward in 2015 by Patel, then a Treasury minister, who wrote in the Telegraph she would end “six-figure payoffs” for public sector workers. But most permanent secretaries, who can be paid more than £200,000 a year, would not be willing to leave for less than £100,000, a Whitehall source said.

“A payoff cap limits the government’s options and strengthens the resolve of those under threat,” a source said.

Since Johnson became prime minister in August, his administration, overseen by Cummings, has been accused of bullying staff in Whitehall.

One senior civil servant with over 30 years’ experience told a colleague: “There is a poisonous, horrible atmosphere – a feeling that retribution could strike at any time for offering the wrong advice to the wrong person.”

Earlier this month No 10 hired 27-year-old Andrew Sabisky to work in an unspecified role, following a call by Cummings for “misfits and weirdos” to apply for civil service roles. Sabisky quit after it emerged that he had previously stated that intelligence is linked to race and argued for the use of brain-enhancing drugs on children.

Following reports earlier this month that some special advisers had sought counselling for stress, Cummings suggested that they should “toughen up”.

One insider familiar with No 10’s thinking said Cummings was serious about replacing people at the top of the civil service who are not deemed up to scratch. On the prospect of a civil service shakeup, which did not materialise at the time of the reshuffle, the source said: “He is biding his time.”

As long ago as 2004, Cummings’s thinktank, the New Frontier Foundation, was writing about the need for “routine purges” to remove “swaths of the top people” which would help “keep everyone on their toes”.

“One of the accepted assumptions of all three parties is that we have a ‘Rolls Royce civil service’ of learned, impartial public servants, and that this system is a great advantage for Britain. We do not agree. The civil service is made up of people fairly typical of the educated elite – they are hostile to competitive markets and favour supranationalism, feeling themselves an enlightened minority beyond the animal passions of the demos.”

It also said: “A serious Conservative government would thoroughly purge the civil service and remove swaths of the top people. Rather than pretend that they are neutral, it would be healthier for Britain to adopt the American system and have routine purges as different political parties gain democratic power. It would keep everybody on their toes.”

One former permanent secretary warned that threats and criticisms against mandarins could make the job of the government much harder.

Lord Kerslake, the former head of the civil service, who was the subject of anonymous N0 10 briefings under David Cameron’s government, said: “If you are looking to change the civil service, you should not declare war on them. It is incredibly unhelpful that this is going on in the media, and it creates the false impression that there are problems between ministers and civil servants across the board.”