The pound rose more than 1% against the dollar on Monday, after the EU’s chief negotiator said a Brexit deal was possible within eight weeks “if we are realistic”.
Sterling later fell back slightly to $1.3042 by the end of the afternoon.
It is the second time in less than a week, Michel Barnier has made comments interpreted as suggesting the EU may be softening its negotiating stance.
The euro also rose against the dollar by around 0.5%.
The possibility that the UK might crash out of the EU without a negotiated settlement has weighed on sterling in recent weeks.
On Monday, Mr Barnier told a business forum in Slovenia : “I think that if we are realistic we are able to reach an agreement on the first stage of this negotiation which is the Brexit treaty within six or eight weeks.”
He has previously identified the end of October as the latest point at which some agreement must be found in order to avoid a disorderly no-deal Brexit.
At the end of last week, Mr Barnier was quoted as saying that the EU was open to discussing the key Brexit stumbling blocks, especially the Irish border issue, which might help pave the way to an overall agreement.
But at the weekend political divisions within the Conservative Party were in the spotlight again, following Boris Johnson’s controversially worded criticism of Prime Minister May’s “Chequers” proposals.
“It just shows that’s the key thing that people want to see: Brexit progress,” said Viraj Patel, a currency strategist at ING in London.
“You have a market that’s heavily short on sterling due to Brexit. It needs that tail risk to be taken off before sterling can rally.”
Connor Campbell, analyst at Spreadex said: “Though, of course, the content of any deal is the thing that really matters, at the moment the pound will take what it can get”.
Figures that showed the British economy growing at its fastest rate for almost a year also boosted sterling’s value.