Filed at the High Court in London, the civil lawsuit is against Barclays, Citibank, Royal Bank of Scotland, JPMorgan and UBS on behalf of pension funds, asset managers, hedge funds and corporate customers.
The banks have already admitted their participation in a cartel and their liability for it, after the European Commission ruled in May that EU competition law had been violated.
Fines of more than $8.5 billion (£6.9bn) from 11 regulators globally have already been handed out.
A similar lawsuit in the US led to a $2.3bn settlement and the UK action group is hopeful of a successful outcome in London.
Michael O'Higgins, former chairman of the Pensions Regulator, who is spearheading the action, said: "The fines imposed on the banks by the European Commission were an important first step, but they will not compensate those who were damaged or suffered losses.
"Just as compensation has been won in the US, our legal action in the UK will seek to return hundreds of millions of pounds to pension funds and other corporates who were targeted by the cartel."
The case is now with law firm Scott+Scott, which led the US case, and is being funded by international lawsuit funders Therium.
Brought under the Consumer Rights Act 2015, the case will be one of the largest facing UK courts and covers UK resident investors and non-UK investors that participated in institutional foreign exchange trading.
UBS has managed to avoid fines from the European regulator in exchange for blowing the whistle on the cartel, but Scott+Scott believes that there is no reason for the bank to be exempt from the civil claims.
David R Scott, managing partner of Scott+Scott, said: "The FX class action in the US led to widespread relief.
"Our experience with this litigation gives us a tremendous advantage in pursuing this case on behalf of victims in the UK and abroad so that they also receive fair and equitable compensation.
"Michael O'Higgins's experience in the pensions industry, which the banks specifically targeted, make him ideally placed to run this claim on behalf of this class."
All the banks declined to comment.