The row ignited when Mr Mitchell was accused of launching a foul-mouthed rant at officers guarding Downing Street as he asked to cycle through the main gates on September 19 last year.
In a letter to MP Keith Vaz, Metropolitan Police Deputy Assistant Commissioner Patricia Gallan confirmed the mounting cost of the inquiry, which has seen statements taken from all 800 officers in the Diplomatic Protection Group.
Mr Vaz said: "It has now taken more than a year to investigate an incident that lasted for 45 seconds, costing the taxpayer an astonishing £237,000, the equivalent to 10 new Metropolitan Police constables.
"It must be in the best interests of the Metropolitan Police Service and Crown Prosecution Service to bring this operation to a conclusion. It is also neither good for the police officers involved or for Andrew Mitchell that this saga continues."
Last week, eight people including five police officers arrested under Operation Alice were re-bailed.
The five constables are from the Diplomatic Protection Group, which is responsible for guarding politicians and foreign dignitaries, and includes a 46-year-old woman present when the row broke out.
The members of police staff are two women aged 46 and 49 who were arrested on suspicion of assisting an offender, and a 23-year-old man who was held in December.
As the anniversary of the incident passed, Scotland Yard came under fire for its handling of the inquiry, with ex-director of public prosecutions Lord Macdonald saying it was ''outrageous'' that the probe continued.
Former home secretary and "personal friend" of Mr Mitchell's, Jack Straw, waded into the row and urged conclusions to be reached.
In her letter to Mr Vaz, Ms Gallan said that as of September 19 this year there were five officers involved in Operation Alice, supported by an officer from the Directorate of Professional Standards (DPS) High Tech Crime Unit and an analyst from the DPS Intelligence Bureau.
Pressure intensified in the wake of the incident when the Daily Telegraph published a police log of the incident, which claimed Mr Mitchell called officers ''plebs'' and swore at them repeatedly for making him walk through a side gate.
The former Tory chief whip insisted he did not use the words attributed to him, and later said he was the victim of a deliberate attempt to ''toxify'' the Tories and ruin his career.
A Channel 4 investigation cast doubt on the officers' account when it revealed CCTV footage which showed there was not a large group of tourists outside the main gate at the time as had originally been claimed.
An email from a civilian witness backing up the police account of events has also been called into question.