The outflows are still, however, far lower than the €7.7 billion withdrawn in June.

Greek business and household deposits now stand at €120.8 billion, around €45 billion lower than at the start of 2015, and are at their lowest level for 12 years. Lower deposit levels make banks more fragile by reducing their capital base.

The cash limit, initially €60 a day, was imposed by Alexis Tsipras’ Syriza government in late June after he unveiled plans to hold a referendum on a bailout offer made by Greece’s EU creditors.

He did it to prevent a full-scale bank run and fears of a Greek euro-exit.

A week earlier, between €4 billion and €5 billion left Greek bank accounts after talks with eurozone finance ministers collapsed.

However, the withdrawal limits themselves fuelled panic, with Greeks fearing the chaos of a currency-switch would wipe out their savings.

The controls are estimated to have cost the Greek economy more than €3 billion in July.

Despite Tsipras agreeing a three-year, €86 billion bailout agreement earlier this month and despite creditors explicitly saying there would be no "bail-in", or private savings confiscations, as in the Cyprus bailout, the €420 limit remains in place.

Individuals are now able to transfer up to €500 per month to a foreign account, while Greek students studying abroad can receive €5,000 per term, however.

As part of the deal, Greece’s banks will be recapitalised before the end of 2015, with €10 billion already made available in an EU co-managed emergency fund.

Meanwhile, the European Central Bank’s emergency liquidity assistance (ELA) programme for Greek banks is now capped at €89.7 billion.

But Estonian central bank governor, Ardo Hansson, a member of the ECB’s governing council, wrote on Wednesday the bailout agreement and gradual easing of capital controls had “helped to increase the confidence of depositors” and that “the volume of ELA has slightly decreased.”

Last week, the ECB lowered the ELA ceiling for Greek banks by €700 million, the first cut since February.