But even though sterling has strengthened, it's still not back to where it was a week ago before Brexit Secretary Dominic Raab resigned last week.
The pound rose by 0.74 per cent, meaning £1 was worth $1.29 dollars shortly before midday today before dropping again to $1.28 at 12:20pm.
It also strengthened against the euro, but not by as much. It rose by 0.48 per cent to a six day high of €1.12 to £1.
The surge comes after Brussels admitted today that the thorny issue of the Irish border could be solved using technology and "Max Fac" solutions at the frontier, as part of the future trade deal between the UK and EU.
But the Brexit boost still hasn't returned the pound to higher levels seen earlier last week, where £1 was worth $1.30 and €1.14.
A 26-page document agreeing a trade deal between the UK and the EU is due to be signed at a summit on Sunday.
But expert Joshua Roberts, from financial risk management consultancy JCRA, warned that the power of the pound could still dip at any moment.
He said: "Despite the positive language, it is difficult to find much in the text that we didn’t know already.
"There is a reasonable chance that the market response is the result of trading algorithms activated by a positive headline, rather than the start of a bigger move."
The confidence boost could help Theresa May get the deal passed through Parliament, but the two parties still haven't reached an agreement over fishing rights and on the status of Gibraltar.
The Sun revealed earlier this week that secret plans were being drawn up in No10 to win back angry Brexiteers who have threatened to vote down Mrs May's deal in the House of Commons.
Many factors can cause the pound to go up or down. In April this year, the pound rose against the dollar to the highest rate it's been since the Brexit vote.
But it took a hit against both currencies in July this year after Boris Johnson resigned from the Cabinet.
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