The pound gained as much as 2.2 per cent, and was last up 2.1 per cent to US$1.2458.
His warning comes ahead of high-level talks between himself and Steve Barclay, the Brexit Secretary, who is due to visit Brussels again on Thursday.
The Taoiseach and Prime Minister have had a detailed and constructive discussion. "And I do see a pathway towards an agreement in the coming weeks".
Across the European Parliament, voices resonated with frustration that one of the most important events for both the EU and the U.K.in decades had turned into a tone-deaf dialogue only three weeks ahead of Britain's planned October 31 departure.
The atmosphere surrounding the negotiations had turned sour in recent days as the two sides blamed each other for their failure to make progress. "Although the joint statement was light on details, it strengthens our expectation that there will be an extension rather than a no-deal Brexit at the end of this month".
The premiers remained in agreement "to reflect further on their discussions and that officials would continue to engage intensively on them". Following the discussions, Varadkar will consult with the EU's Brexit negotiating taskforce.
Brexit Secretary Steve Barclay will meet his European Union counterpart Michel Barnier in Brussels on Friday, with the visit put back 24 hours following Johnson´s hastily arranged meeting with Varadkar.
Striking a positive tone at Liverpool airport, Varadkar said the main issues remain ensuring that any long-term agreement has the consent of the people of Northern Ireland and ensuring no customs border on the island of Ireland.
Johnson has proposed limited customs inspections away from the frontier, but Varadkar insists any such checks will threaten peace in the region, which suffered decades of terrorism.
A senior diplomat dismissed the Times report as "spin" in the negotiations, while another official said that "no bold new offer is coming from the European Union side at this stage".
"All of those who are not playing his game are traitors, collaborators or surrenders", said the former Belgian prime minister.
Chancellor Merkel was reported to have said that "the United Kingdom can not leave without leaving Northern Ireland behind in a customs union and in full alignment forever".
While Ireland would be very badly affected by a no-deal Brexit, the relative importance of Ireland in the negotiations up-ends nearly a thousand years of history in which Dublin has had a much weaker hand than London.
The Italian politician said an extension would be approved if it paved the way for a second referendum or a general election.
Ireland's position will guide the EU's remaining 27 member states.
Following these last-ditch talks between Irish Taoiseach Varadkhar and UK PM Johnson, Varadkhar is now set to meet EU's chief Brexit negotiator Barnier and other key European Union stakeholders on Friday and UK's Brexit Secretary will also meet with Barnier and his negotiating team and GBP is higher as markets have the sense that they may have rekindled potential for compromise.