In his letter Sir Ed called on the police to fully investigate the claims and issue fines to anyone found to have broken lockdown laws.

In the letter to Dame Cressida, he wrote: “It is now vital that you take urgent action to investigate potentially unlawful behaviour on the part of all those who attended the party, including Boris Johnson.

“On the day of the Downing Street garden party, the Metropolitan Police Twitter account published a tweet which stressed the importance of continuing to follow the lockdown rules in place at the time, which included not meeting with more than one other person outdoors.

“It is clear from the descriptions of the Downing Street Party that it failed to meet these criteria. It also was clearly not a work meeting – given the instruction to “bring your own booze”. It was therefore almost certainly an illegal gathering.”

‘Treat everyone equally under law’

Sir Ed pointed out that more than 17,700 people had been fined by the Met for breaching Covid laws during the pandemic and he added that it was vital everyone was treated equally under the law.

Commenting on the importance of an independent police investigation he said: “People have sacrificed so much during this pandemic, from cancelling weddings to not being able to say goodbye to their loved ones in hospital.

“The police must reassure the public that justice will be done and there isn’t one rule for them and another for Boris Johnson and his colleagues in Downing Street.”

Allegations regarding the event on 20 May 2020, emerged on Monday afternoon, when an email from Martin Reynolds, the Prime Minister’s Principal Private Secretary, was published.

In it, Mr Reynolds, a senior civil servant, who has run Mr Johnson’s private office since October 2019, wrote: “Hi all. After what has been an incredibly busy period it would be nice to make the most of the lovely weather and have some socially distanced drinks in the No10 garden this evening. Please join us from 6pm and bring your own booze.”

Following the leak of the email a spokesman for Scotland Yard said the force would not be launching an immediate criminal probe.

“The Metropolitan Police Service is aware of widespread reporting relating to alleged breaches of the Health Protection Regulations at Downing Street on 20 May 2020 and is in contact with the Cabinet Office.”

It is understood that Ms Gray – who is looking at allegations of eight illegal gatherings by staff from government departments – has been in contact with Scotland Yard in recent days to discuss material she has found.

A source close to the investigation said if police were handed significant material that reached the “necessary evidential threshold” they may launch their own inquiry at that stage.

It is unclear whether the launch of the criminal investigation would mean that Ms Gray’s probe would be put on hold.

Police ‘have duty to investigate’

But there is growing concern in some quarters that the delay is damaging the Met’s reputation.

Former Met Police Chief Superintendent Dal Babu said: “It’s not a difficult case to solve, you’ve got a secure scene, you’ve got CCTV, it’s relatively straightforward.”

Another senior police source added: “The police are independent of government. If there is an allegation of criminal wrongdoing they have a right and a duty to investigate.

“Their general position has been to say they won’t look at things retrospectively, but there is prima facie evidence to suggest there was a breach so if the Met wants to avoid accusations of political manoeuvring they need to announce an investigation, and soon.”