Home Secretary Priti Patel has said she regrets the resignation of the Home Office's former top civil servant, Sir Philip Rutnam, who stepped down amid bullying allegations against her.

In an internal email to Home Office staff, Ms Patel thanked Sir Philip for a "long and dedicated career of public service" but said the department must now "come together as one team".

Sir Philip, the department's most senior civil servant, quit on Saturday after accusing Ms Patel of orchestrating a "vicious" campaign against him, of lying about her involvement in it and of creating a climate of fear among her officials.

Sir Philip said he was quitting as permanent secretary of the Home Office to "protect the health, safety and wellbeing" of the 35,000 staff in the department.

In an apparent denial, Ms Patel said in the email she does "care about the wellbeing" of all her staff.

The email, which was cosigned by Sir Philip's temporary replacement Shona Dunn, went on: "We also recognise the importance of candour, confidentiality and courtesy in building trust and confidence between ministers and civil servants.

"Both of us are fully committed to making sure the professionalism you would expect to support this is upheld."

The email added: "We both regret Sir Philip's decision to resign.

"He had a long and dedicated career of public service for which we thank him."

Following the allegations, Boris Johnson asked the Cabinet Office to “establish the facts” of the case.

Cabinet Office minister Michael Gove confirmed the action being taken following an urgent question from Labour leader Jeremy Corbyn.

Ms Patel's email follows an outpouring of support for Ms Patel from her Conservative colleagues, including the Prime Minister and his de facto deputy Mr Gove.

In the Commons on Monday Mr Gove told MPs: "Allegations have been made that the Home Secretary has breached the ministerial code.

"The Home Secretary absolutely rejects these allegations.

“The Prime Minister has expressed his full confidence in her, and having worked closely with the Home Secretary over a number of years, I have the highest regard for her, she is a superb minister doing a great job.

“This Government always takes any complaints relating to the ministerial code seriously, and in line with the process set out in the ministerial code the Prime Minister has asked the Cabinet Office to establish the facts."

Mr Gove said the Government would not comment on an individual matter, in line with policy, before praising the Home Office ministers and civil servants.

Speaking on Sunday, Mr Johnson expressed his full confidence in Ms Patel, who he promoted to one of the great offices of state after she had previously been sacked from the Cabinet by Theresa May.

However, some Tory MPs have questioned how much longer she can carry on in the job, while Labour has complained the inquiry into her conduct - to be carried out by the Cabinet Office - is not fully independent.

Ms Patel is a "fantastic Home Secretary," the prime minister said.

"It is never an easy job, as anyone who has been Home Secretary will testify.

"It is one of the toughest jobs in Government."

He added he was "full of admiration" for the work of the civil service:

"We politicians could not begin to accomplish things without the fantastic, absolutely brilliant alpha minds in the civil service.

"We depend on them."

The Home Office declined to comment on the email, which was leaked to journalists.