Mr Mitchell, who resigned from his post over the incident in Downing Street, has called for a full inquiry.
On Tuesday, Channel 4 News accused the officer of falsely claiming to have seen the events in an email to his MP.
The Metropolitan Police Federation later strongly denied any "conspiracy".
Channel 4 News alleged the police officer posed as a member of the public who witnessed the row in which Mr Mitchell was said to have called police "plebs".
Mr Mitchell has always denied using the word but has admitted he had lost his temper and swore at the officers after they refused to let him cycle through the main gate to Downing Street.
A spokesman for No 10 said of the latest claims: "Any allegations that a serving police officer posed as a member of the public and fabricated evidence against a cabinet minister are exceptionally serious.
"It is therefore essential that the police get to the bottom of this as a matter of urgency."
He added: "We welcome [Metropolitan Police commissioner] Bernard Hogan-Howe's commitment to achieve that aim."
John Tully, chairman of the Metropolitan Police Federation, which represents officers in the Met Police, said: "The Metropolitan Police Federation unequivocally and categorically refutes any allegation that it was part of a conspiracy to unseat a cabinet minister."
A Diplomatic Protection Squad officer was arrested on Saturday by officers investigating how national newspapers came to publish police records of the incident.
Although the arrested officer was not on duty at the time, they claimed to have witnessed the incident - a claim now being probed by the Independent Police Complaints Commission.
The Conservative MP told Channel 4 News he had been "really shocked" to learn of its allegations that the original newspaper coverage of the claim he had used the word "pleb" had been corroborated by the email from the officer pretending to be an eyewitness.
"I always knew that the emails were false, although extremely convincing," Mr Mitchell, MP for Sutton Coldfield, said.
"If you'd told me on 19 September [the night of the row] that the experience I have had since then, the revelations that have since come to light, could take place in Britain today, I simply would not have believed you.
"And it's certainly shaken my lifelong support and confidence in the police.
"I believe now that there should be a full inquiry so that we can get to the bottom of this, so that everyone can have confidence that this sort of thing won't happen again."
London Mayor Boris Johnson said: "An allegation that a serving police officer posed as a member of the public whilst fabricating evidence is a matter of the utmost gravity.
"I know that the Metropolitan Police Commissioner is committed to establishing the truth here, as soon as possible."
BBC political editor Nick Robinson said Mr Johnson's comments were the first time there had been suggestion of a conspiracy involving police officers.
Channel 4 News broadcast CCTV footage which it said cast doubt on the official police log of the night of the row.
The footage shows the MP with his bicycle talking to three officers by the main gate at Downing Street for about 20 seconds. He then wheels it over to the side gate and exits.
Mr Mitchell said on Channel 4 News that his first reaction was "there's not really much of an altercation" when the story about his dealings with the police emerged.
"There were three phrases above all which were hung around my neck for the following 28 days every day in the press which were used to destroy my political career and were used to toxify the Conservative Party," he added.
Before the footage was broadcast, Mr Hogan-Howe had told the BBC that he had seen no reason to doubt the original claims by the Downing Street police officers.
MP Keith Vaz, chairman of the Home Affairs Select Committee, said he planned to write to the Met commissioner to ask for a full explanation of what happened.
Mr Mitchell told Channel 4 News he would never call anyone the name which he was accused of using, adding, "anyone who know me well would know that it is absolutely not in me to use phrases like that".
Asked why he did not give a more detailed account earlier, Mr Mitchell said: "Well, when the story broke, the decision was made that I would apologise for what I did say, and my apology was accepted; there was no police complaints and that we would let it lie.
"Now with the benefit of hindsight, that was clearly the wrong decision."
Following the airing of the Channel 4 News report, Health Secretary Jeremy Hunt tweeted: "Incredibly concerned at v serious C4 Dispatches suggestion that A Mitchell was stitched up, never believed he used p-word anyway."
Conservative MP David Davis told the BBC: "He has suffered a real injustice. His reputation has been traduced, he's lost his job, his career's come to an end and to all intents and purposes that's pretty tough on the basis of something that may not now be quite the way it looked at the beginning."
Allegations that a police officer falsely claimed to have witnessed former Chief Whip Andrew Mitchell calling police "plebs" are "exceptionally serious", No 10 says.