Sterling jumped 2.1 per cent against the dollar to $1.269 and 1.8 per cent against the euro to €1.149.
The gains eclipsed those made yesterday, which resulted in the pound’s best daily rise since March.
Friday’s surge came after British and EU negotiators agreed to intensify Brexit talks, in a major boost for Boris Johnson’s hopes of getting a deal.
EU officials confirmed at lunchtime that negotiations will be entering a “tunnel” – Brussels jargon for intense private negotiations where leaks are kept to a minimum.
Despite the news, Donald Tusk, the European Council president, warned that current UK proposals are neither “workable” nor “realistic”.
However, he also said he has heard “optimistic messages” that a Brexit deal can be reached.
Neil Wilson, chief market analyst at Markets.com, said sterling’s rally over the last two days was “astonishing” but the ride is not yet over.
“Now that negotiations are in the tunnel phase, we should anticipate a lot less news flow but there will be just as much speculation as ever,” he said.
“Of course, this rally is built on shaky foundations and is susceptible to a crash if the negotiations don’t produce a deal for MPs to vote on.”
Stocks also rose around the world on the back of speculation that the US and China may be closer to reaching a trade deal after 15 months of damaging rhetoric and tariff rises.
Markets in the US, Japan, the UK, Germany and France all posted strong gains.
Donald Trump struck a positive tone ahead of his meeting with Chinese officials on Friday.
The US president tweeted: “Good things are happening at China trade talk Meeting. Warmer feelings than in recent past, more like the old days. I will be meeting with the vice premier today. All would like to see something significant happen!”
In London, the globally focused FTSE 100 rose less than other European markets, in part due to the pound’s renewed strength. Many multinational firms earn revenues in other currencies before converting them into sterling, which means their bottom lines are given a foreign exchange boost when the pound is weak.
The more domestically focused FTSE 250 soared more than 3 per cent in response to the positive noises emanating from Brussels.
A UK government spokesperson and an EU Commission spokesperson both separately described the morning’s meeting as “constructive”, as did Michel Barnier, the EU’s chief negotiator.
“Brexit is like climbing a mountain,” Mr Barnier said. “We need vigilance, determination and patience.”
A European Commission spokesperson said: “The EU and UK have agreed to intensify discussions over the coming days.
“The EU’s position remains the same: there must be a legally operative solution in the withdrawal agreement that avoids a hard border on the island of Ireland, protects the all-island economy and the Good Friday (Belfast) Agreement in all its dimensions, and safeguards the integrity of the single market.”
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