It has been sent just three days after the Home Secretary was allowed to keep her job, despite an independent investigation concluding her bullying broke the ministerial code.
Despite praising civil servants for their dedication during the pandemic, it also reminds them not to leak private conversations.
The letter, co-signed by Simon Case, the new Cabinet Secretary, comes amid the continuing furore over Mr Johnson’s unprecedented decision to stand by Ms Patel, despite the damning conclusions on her behaviour.
Alex Allan, his adviser on ethics, quit in protest, after the prime minister overturned his report by arguing the examples of bullying were not clear.
There is also anger over Mr Johnson’s message to Conservative MPs, urging them to “form a square behind the prittstar” – to shore up her position.
Lord Wilson, a former head of the civil service, said the instruction was part of a pattern that threw into question the “principle of ministerial responsibility”.
“There is a growing string of cases where ministers wrongly disclaim responsibility, whether it be the harassment of civil servants or intervening improperly in the planning process or blaming others for the exams fiasco or poor handling of the pandemic,” he wrote.
“Forming a square around a colleague who is in trouble sounds tribal rather than good governance.”
The new letter states: “Given the unprecedented challenges we currently face as a nation, relationships of mutual trust and respect between politicians and their officials are paramount.
“This includes keeping internal conversations private. We should all be able to speak freely and honestly about matters of state.
“We should also feel able to speak constructively about things that are not working, so that we can fix them together promptly.”
Ms Patel is now under fire for briefing a friendly newspaper that she will shake up the Home Office by forcing officials to work some weekends and introducing performance reviews for senior civil servants.
Dave Penman, head of the FDA union, which represents civil servants, said: “To suggest the Home Secretary is now responsible for performance reviews for the ‘senior ranks’ is simply fiction.
“It is also insulting to suggest that the civil service does not respond to demands or is stuck in a 9-5 culture, as the anonymous briefings suggest.”