Dame Cressida Dick will continue to lead the Metropolitan Police Service until 2024, the Home Secretary Priti Patel has confirmed.

A two-year extension to Dame Cressida’s current fixed-term appointment as Commissioner – which was due to end in April 2022 – was granted by the Queen, the Home Office said on Friday.

It comes after the force’s officers gave their “full support” to her after critics called for her to be replaced.

A number of high-profile figures had signed an open letter to the Prime Minister accusing the Commissioner of “presiding over a culture of incompetence and cover-up” following reports she had been offered a two-year extension to her contract.

Home Secretary Priti Patel said: “I am pleased to announce that Dame Cressida will continue to lead the Metropolitan Police until April 2024 and wish to thank her for her service to date”, adding that the extension to her contract will provide “continuity and stability as we emerge from the coronavirus pandemic and recruit 20,000 additional police officers”.

Mayor of London Sadiq Khan said he supported the decision, adding: “This will provide the experienced and strong leadership we need as our city emerges from the pandemic.”

The letter sent earlier this week urged Boris Johnson to replace the Commissioner, arguing that she “must be properly investigated for her conduct, along with predecessors and those in her inner circle, who she appointed and who have questions to answer”.

Signatories included Baroness Doreen Lawrence, Lady Diana Brittan, former Tory MP Harvey Proctor and broadcaster Paul Gambaccini – who have all expressed disappointment or criticism of the police over cases affecting them.

Earlier on Friday, Ken Marsh, chairman of the Metropolitan Police Federation, which represents more than 30,000 officers in London, said Dame Cressida had the “full support of the rank and file”.

He told the PA news agency her leadership had been “excellent”, while her “ability to communicate with officers of all ranks is quite incredible”.

Dame Cressida said: “I am immensely honoured and humbled to have been asked to extend my time as Commissioner for a further two years. I am proud to continue to serve my city.

“I look forward to continuing to work with my dedicated, courageous colleagues and the public to create an even more visible, stronger and professional Met. We will strive to prevent and reduce violence and the crimes Londoners care most about, bring more criminals to justice, and protect, support and build the confidence of all our communities.

“I’d like to thank the Mayor, the Home Secretary and the Prime Minister for the confidence they have shown in me. I am acutely aware that there are many excellent leaders in policing.”