He was responding to claims by Brexit campaigner Nigel Farage that former British prime minister Tony Blair and others, including Mr Varadkar, were trying to “force the Brits to do it again”, knowing other states would leave if Brexit proceeds.
The Taoiseach was speaking at a special debate on the future of the EU at the European Parliament in Strasbourg, France, being the first national leader to be invited. He thanked the EU for its solidarity with Ireland over Brexit and stressed there can be “no back- sliding” on a soft border.
While acknowledging difficulties within the EU, Mr Varadkar said the rise of populism and extremism showed the need to ensure “the European ideal has been tested, but not broken”.
His comments were welcomed by European Commission president Jean-Claude Juncker and European Parliament chief Brexit negotiator Guy Verhofstadt, who said “We are all Irish” when it comes to Brexit.
However, they were rounded on by former UKIP leader Mr Farage, who provoked cheers and jeers in equal measure by attacking the Taoiseach’s views.
After labelling Mr Varadkar “a European unionist, whatever the cost to Ireland” and only being popular in the European Parliament as “you’re useful, because you’ve helped with the delay of Brexit”, Mr Farage accused the Taoiseach of being involved in a “plot” to undermine Britain’s departure from the EU.
“You are part, of course, of a bigger attempt to prevent Brexit. You don’t want Britain to leave, because you know others will too.
“I don’t want a second referendum on Brexit, absolutely not, but I fear you’re all working together with [Tony] Blair and [former Liberal Democrats leader, Nick] Clegg. If you force the Brits to do it again, there’ll be a different outcome,” he said.
The claim has been repeatedly made by hardline Brexit supporters in recent months, due to the continuing difficulties in Britain and the EU agreeing on a deal.
However, later, speaking to reporters alongside European Parliament president Antonio Tajani, Mr Varadkar insisted no plot exists.
“I’ve never met Tony Blair and I’m certainly not involved in any plot for a second referendum.
“I don’t think it would be constructive or helpful for the leader of another country to be advising that other country on whether they should or should not have a second vote. It has to be a matter for the UK parliament and the people of the United Kingdom. A decision on a second referendum must only be one made by parliament or UK people. It may be counter-productive,” said Mr Varadkar.
Asked about the possibility of a second referendum, Mr Tajani said: “If the British want to change their position, fine, I agree.”
On Tuesday, both Mr Juncker and European Council president Donald Tusk said “our door is still open” if Britain wants to U-turn on Brexit and hold a second referendum.