Six major banks caught up in the investigation into rigging the currency markets are being pressed by the regulator to agree to fines – possibly of as much as £1.8bn – in the next eight weeks.

The Financial Conduct Authority (FCA) held discussions with each of the banks this week to warn them that they faced multimillion-pound penalties that could surpass the £160m levied on the Swiss bank UBS for rigging Libor – the biggest fine the UK regulator has imposed.

Royal Bank of Scotland, HSBC, Barclays, Citi, UBS and JP Morgan declined to comment on the talks with the FCA, which is run by Martin Wheatley and which has been investigating the £3.5bn currency markets for two years.

The regulator, which also refused to comment, is said to be keen to avoid the protracted talks that characterised the long-running investigation into Libor rigging. Barclays was the first bank to be fined in 2012, paying £290m in the UK and US for manipulating the benchmark interest rate. There have been six subsequent fines but the FCA and US investigators have yet to complete their regulatory actions against some other banks.

While the FCA is working on a coordinated settlement with the banks being investigated for currency rigging, it is also edging closer to concluding the Libor inquiry, which could result in other fines and reprimands this year.

It is also uncertain whether the banks will agree to a settlement, especially without agreement from the other regulators around the world also involved in investigations, particularly in the US where fines are larger. This week Andrew Bailey, deputy governor of the Bank of England, called for a “cards on the table” approach from regulators.

A Sky News estimate of £2bn of aggregate fines was later followed by an estimate from Reuters of £1.8bn, which was likely to take into account discounts applied for settlements,

The allegations over the manipulation of currency markets were exposed after the Libor scandal shed light on the potential rigging of other financial markets – including in gold and silver – which were largely unregulated before the financial crisis. The fines and settlements for fixing foreign exchange rates are expected to bring the release of a wave of emails and electronic chat messages similar to those published when Libor rigging fines were levied, detailing how traders offered each other bottles of champagne and illustrating the cavalier way in which traders regarded their actions.

One Libor submitter declared himself “like a whore’s drawers” while others were found referring to each other as “big boy” and offering to “pay you … whatever you want”.

In February, Wheatley warned that the banking allegations were “every bit as bad as they had been with Libor” as the industry braced for another hit to its reputation.

Mark Carney, the Bank of England governor, has also warned about the damage to the banks’ standing.” This is as serious as Libor, if not more so because this goes to the heart of integrity of markets,” he said in March.

The banks may favour an industry-wide settlement as it would avoid the need for one of them to go first. Days after Barclays settled over Libor fixing, it announced the resignation of its chairman, Marcus Agius, chief executive, Bob Diamond, and chief operating officer, Jerry del Missier.

But while bank shares rose on Friday on the prospect of a less-damaging industry-wide settlement, banks have also been warned about the impact of the fines on their business. RBS, for instance, admitted in August that it could take a “material” hit to its profits as a result of any foreign exchange settlement.

The investigation into the foreign exchange markets is thought to centre on the way a benchmark known as WM/Reuters operates. It is used to price several currencies at 4pm each day, and the investigators appear to be focused on allegations that traders put in client orders before a frenetic 60-second window when the price is set.

The inquiry has also drawn in the Bank of England, which has appointed Lord Grabiner QC to scrutinise any involvement by its officials who, it has been alleged, knew that traders were sharing information about their clients’ positions. The Bank has suspended one person, while at least 20 foreign exchange dealers are thought to have been suspended.

The rigging of foreign exchange markets is expected to become a criminal offence by the end of the year after the Treasury started consulting on new rules this week.

Biggest libor fines imposed by UK City regulator

• Swiss bank UBS: fined £160m in December 2012.

• Dutch bank Rabobank: fined £105m in October 2013.

• Lloyds Banking Group: fined £105m in July 2014.

• Royal Bank of Scotland: fined £87.5m in February 2013.

• Barclays: fined £59.5m in June 2012.

• ICAP, money broker: fined £14m in June 2014.

• RP Martin, money broker: fined £3.6m in May 2014 but this was reduced to £630,000 after its financial position was taken into account.