The home secretary, Priti Patel, is under pressure on multiple fronts following a claim that Boris Johnson’s failure to conclude a seven-month bullying inquiry into her conduct is damaging relations across Whitehall. The allegation was sent to the prime minister by the FDA union as Patel’s allies said they suspected other ministers may be behind attempts to discredit Home Office plans for asylum seekers by leaking details to the media. Dave Penman, the union’s general secretary, told Johnson that the delay in publishing the inquiry’s findings was eroding trust between ministers and senior civil servants. “I would urge you to recognise the long-term damage that is being done to the relationship between ministers and civil servants by these delays and address these issues as a matter of urgency,” Penman wrote in a letter seen by the Guardian. The Cabinet Office inquiry was launched on 2 March by Michael Gove, who told parliament: “It is vital that this investigation is concluded as quickly as possible in the interests of everyone involved.” Patel is alleged to have mistreated staff and clashed with senior officials in three departments, including in her role as home secretary. She has denied all the claims. Several reports have claimed that the inquiry, conducted under the ministerial code, has been completed and is waiting for the prime minister’s signature. Penman wrote that senior civil servants were concerned that ministerial inquiries, which provide no transparency or timeframe for conclusion, may not be free from political interference. “Seven months on, it will be hard to reach any conclusion other than that justice has already been denied and that the continued delay to the process is driven solely by political considerations,” he wrote. Trust between government departments was eroded this week after several leaks were made over Home Office plans for asylum seekers arriving in the UK. Sources in the department said they were concerned that officials from rival ministries were behind revelations that officials had considered detaining people in centres in locations such as Ascension Island and Papua New Guinea. There are concerns that “blue sky” ideas, some of which originate with the prime minister’s chief adviser, Dominic Cummings, are being leaked to damage both the Home Office and Patel. Andrew Bridgen, the MP for North West Leicestershire, said some of the briefings may have come from potential rivals in any future leadership challenge. “Some people are worried because they see Priti as a future leader of the Conservative party, and they know that these policies are incredibly popular in the party so they want to ridicule them,” he said. Documents seen by the Guardian suggest the government has for weeks been working on “detailed plans” that include cost estimates of building asylum detention camps on the south Atlantic islands of Ascension and St Helena, as well as Moldova, Morocco and Papua New Guinea. Disused ferries or abandoned oil rigs have also been considered. One source said: ‘These stories have not been coming from the Home Office. One has to wonder who is leaking them and why.” Patel’s allies said the creation of remote asylum processing centres was not something being planned in the short term, and that it remained more likely that the Home Office would instead reconsider opening up disused prisons and detention centres, such as Morton Hall in Lincolnshire. The home secretary will give details of her migration policy in a speech on Sunday to the Conservative party conference. Asked to respond to the FDA’s letter, a UK government spokesperson said: “The process is ongoing. The prime minister will make any decision on the matter public once the process has concluded.”