An armed Metropolitan police officer who was on duty in Downing Street on the night of the Plebgate incident involving the former chief whip Andrew Mitchell texted a colleague two days later to say that she could "topple the Tory government".

The text is published in a lengthy report by the Metropolitan police into Operation Alice, its investigation into the incident in Downing Street on 19 September 2012, which ended Mitchell's cabinet career. The Met has also released CCTV footage of the incident.

Deputy assistant commissioner Patricia Gallan, who was in charge of the Operation Alice investigation, said that allegations that officers had conspired to falsify statements had "damaged public trust and confidence in us".

Mitchell was forced to stand down as chief whip after armed officers on duty in Downing Street claimed that he described them as "fucking plebs" when they declined to allow him to wheel his bike through the Downing Street gates at the end of the day.

Mitchell admitted swearing in the presence of the officers as he told them they were meant to help people working in Downing Street. But he insisted that he never described the officers as plebs.

Friends of Mitchell believe the report shows that police officers deceived the Met on a large scale as they sought to reinforce their account of the incident. The investigation led to the dismissal of four police officers, one of whom was sent to prison.

The report found that PC Gillian Weatherley, who was one of the four officers to lose their jobs after disciplinary hearings, texted a colleague two days after the incident to declare that she could topple the government. Weatherley witnessed, but did not overhear, the incident between Mitchell and her colleague PC Toby Rowland.

In the text, sent on 21 September to a colleague known as Officer 18, Weatherley wrote: "This will make you feel better, I'm the officer that stopped the chief whip leaving Downing St in Wednesday. He didn't swear at me but Toby that let him out the side gate. I could topple the Tory government x."

In her disciplinary hearing Weatherley explained that she had known the recipient of her text for 20 years and the message was office banter. But a month later, on 21 October 2012, a text message was sent from her phone number to a neighbour called Nick. It read: "Not today but I'm at the front gates tomorrow so I still have time to bring the government down thanks for no graffiti."

The report said that Weatherley said the text was part of a friendly conversation. "PC Weatherley denied that these texts showed any sinister motive on her part in relation to her conduct under investigation," it said.

Weatherley lost her job after she failed to provide an honest account of her role in the handling of an email by Rowland that described the incident. She denied having passed on Rowland's email when she had in fact sent a picture of the email to a colleague. This was passed to the Daily Telegraph.

Gallan said of the report: "At the heart of this investigation were very serious allegations that police officers had conspired together to lie and falsify statements against a cabinet minister. I have no doubt these allegations have damaged public trust and confidence in us.

"The police service is here to serve the public, without fear or favour, with honesty and integrity. Where our staff fall short of those standards they must be held to account. We wanted these discipline boards to be held in public, but legally we were unable to direct that this happened.

"Ultimately, four police officers have been dismissed from the MPS, one of whom was sent to prison. Every serving police officer has cause to feel let down by those colleagues who fall below the standards we all strive to uphold."