Cairns' lawyers told the Daily Telegraph that in July they laid a complaint with police about Vincent's match-fixing.
Detectives from Scotland Yard could pursue a criminal case against Vincent after receiving the complaint, which is based around his confession to fixing cricket matches while playing in England for Lancashire and Sussex.
"I can confirm that on 2 July 2014 I referred Mr Vincent's serious criminal activities to the Metropolitan Police Service with a view to his prosecution," said Rhory Robertson, partner at Collyer Bristow, solicitors acting for Cairns in England.
"Our legal system has as its core the principle that all people are treated equally before the law. No one, including the MPS [Metropolitan Police Service] and the CPS [Crown Prosecution Service], can be unreasonably selective as to when and against whom they apply the law. Lou Vincent's admitted offences are serious and have so far gone unsanctioned. This failure to prosecute is unacceptable."
Cairns is living in New Zealand and facing financial ruin over his legal battles. His friend and former team-mate Dion Nash told the Herald recently that Cairns was driving a council truck in Auckland and water-blasting bus shelters for $17 an hour.
In July, Vincent confessed to match-fixing and was banned from the sport for life.
The Telegraph reported that Vincent's evidence to the anti-corruption police had formed the basis of a police investigation into Cairns.
"Mr Vincent has committed serious criminal offences - yet no criminal charges have been brought. Why has the ECB (England Wales Cricket Branch) failed to have the CPS prosecute Lou Vincent? How is the Vincent case different to the successful prosecutions of others?" Robertson said to the Telegraph.
"David Richardson, the chief executive of the ICC, stated as recently as 1 July 2014 that 'where suspicious activity is uncovered, no stone will be left unturned to bring those involved to justice'.
On the same day David Collier, [former] chief executive of the ECB, announced that the Lou Vincent investigation had 'been brought to a satisfactory conclusion and that the ECB's action highlights our resolve to keep cricket clean'.
"It is said that Lou Vincent has estimated his earnings from cheating at around 150,000 pounds. He has admitted to match fixing for a period spanning six years. In 2011 international cricketers Butt, Amir and Asif were convicted of conspiring to fix matches as was Mervyn Westfield in 2012.
"All received prison sentences. Their financial 'rewards' for fixing were substantially less than the amounts received by Mr Vincent."
