CCTV footage was released by Whitehall of the incident in which Mr Mitchell, who lost his job over an alleged tirade against police officers in Downing Street, was prevented by officers from cycling through the main gates in September.
The footage, which had no sound, cast doubt on a key point in a leaked police log – that the incident was witnessed by several members of the public.
The pictures showed one man outside the gates at the time of Mr Mitchell's confrontation.
John Randall, deputy to Mr Mitchell, was the local MP contacted by the alleged witness, who did not mention he was a serving police officer.
However, UK Government sources said he acted correctly by passing on the alleged witness's statement that appeared to corroborate almost word for word the official police log – that the ex-Cabinet minister had sworn at police officers and called them "plebs".
At the weekend, a diplomatic protection squad police officer was arrested by officers investigating how newspapers came to publish police records of an incident in Downing Street.
In a statement, No 10 said: "Any allegations 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 the police get to the bottom of this as a matter of urgency. We welcome Bernard Hogan-Howe's commitment to achieve that aim."
Mr Mitchell, a Midlands MP, claimed he was the victim of a "stitch-up" and demanded a "full inquiry so we can get to the bottom of this".
He said: "There were three phrases 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.
"I never said phrases like that at all. Anyone who knows me well would know that it is absolutely not in me to use phrases like that."
Earlier, Mr Hogan-Howe, the Metropolitan Police Commissioner, said he was standing by the officers in the controversy.
He said: "There is more to this than meets the eye. I'm afraid I'm constrained in explaining that and I hope when people hear the full story, they will support what we've done."