By Jemima Kelly

LONDON, June 30 (Reuters) - Sterling climbed for a third day on Thursday, but traded in tight ranges as investors waited for new developments on Britain's shock decision to leave the European Union, which sent the currency to a 31-year low.

The pound tumbled almost 8 percent last Friday, the steepest daily decline in the post-1973 floating-exchange-rate era, after the result of Britain's referendum on EU membership stunned markets. Those losses continued into Monday, with sterling shedding another 3 percent and markets firmly in risk-off mode.

But sterling has recovered almost 2 percent in the past three days against the dollar.

On Thursday sterling was 0.3 percent higher at $1.3460, leaving it more than 3 U.S. cents higher than Monday's low of $1.3122. It was also 0.3 percent higher against the single currency at 82.60 pence per euro.

Investors were drawing some reassurance from the fact that British politicians were not rushing to trigger the Article 50 mechanism for a state to leave the EU, despite European leaders telling Britain to act quickly after last week's referendum.

"Investors everywhere are a bit unsure what the UK's departure from the EU will look like and what it means, a mindset that may now last a while," said Societe Generale macro strategist Kit Juckes.

Data showing just how big Britain's hefty current account deficit is will be closely watched when it is published at 0830 GMT, along with final gross domestic product data.

One of the reasons investors had been so worried about a Brexit was that it could put at risk the large investment flows Britain relies on just to fund that deficit.

Bank of England Governor Mark Carney will be watched for clues on interest rates, when he gives policy guidance at 1500 GMT - his second speech since the Brexit vote.

Analysts said money markets were almost fully priced for a rate cut by the Bank of England by the end of the year and around a 50 percent chance of one by August, which should keep sterling weak. Before the vote, they suggested only a 20 to 30 percent chance of a cut by year-end.

"We expect the BoE to ease monetary policy further in the coming months, either through lowering interest rates and/or restarting QE, and/or expanding their 'Funding for Lending' scheme," wrote Bank of Tokyo-Mitsubishi UJF currency economist Lee Hardman in a note to clients.

"Further BoE monetary easing should keep downward pressure on the pound through the rest of this year." (Editing by Janet Lawrence)