Eurozone finance ministers met Monday to discuss ways of reducing the economic impact of Britain's decision to leave the European Union, in their first meeting following last month's shock referendum outcome.

Britain is not a member of the 19-member currency bloc but, as one of the EU's three largest economies, it is an important trading partner. The June 23 vote to leave the EU has led to market volatility and a sharp fall in the pound, amid uncertainty over the steps ahead.

EU Economy Commissioner Pierre Moscovici said he would present the ministers with a first assessment of the effect Brexit could have on the eurozone economy, which has battled with high unemployment and sluggish growth.

"These are not forecasts, these are reflections," Moscovici said, adding: "They show that the impact could be significant and that it is therefore necessary to work on reducing it."

"It must be clear that Brexit will lead to changes relating to growth," Austrian Finance Minister Hans Joerg Schelling added.

The ministers' talks came hours after British Home Secretary Theresa May emerged as the only candidate to succeed Prime Minister David Cameron, who tendered his resignation following the Brexit vote.

The development brought welcome clarity, several ministers said ahead of their talks, while Moscovici expressed hope that it would give the "impetus and strength" for Britain to open formal exit negotiations - a move that Brussels would like to see happen soon.

Cameron announced that he would hand over the premiership to May by Wednesday evening.

The Eurogroup of eurozone ministers was also expected to discuss how to proceed against Spain and Portugal for breaching EU budget rules, before the issue goes before all 28 EU finance ministers on Tuesday.

Last week, the European Commission found that Madrid and Lisbon had failed to take effective action to whittle down their deficits, bringing the countries a step closer to being penalized.

Members of the eurozone should limit their deficits to 3 per cent of gross domestic product. Portugal was supposed to reach this goal last year, while Spain has until the end of 2016, but is not on track.

The issue is sensitive, with Portugal expected to bring its deficit in line this year and Spain grappling with political paralysis after two elections within seven months have failed to produce an outright winner.

"I think we are all in agreement here that we have to apply the rules we set ourselves, which include enough flexibility," German Finance Minister Wolfgang Schaeuble said.

But Moscovici noted that, while it is crucial to ensure the credibility of the EU's rules, these are "not a punishment." There are "intelligent" means to apply the rules without harming growth and job prospects in Spain and Portugal, he added.

"It would be sufficient to have the finding that they were in breach. We are not interested in having sanctions applied to them," Irish Finance Minister Michael Noonan added.

The commission had indicated last week that fines for both countries could be whittled down to zero.

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