Sir Keir Starmer has said the prospect of a referendum on Irish unification is “absolutely hypothetical” and “not even on the horizon”.
The Labour leader, who could be the UK’s next prime minister, strongly rejected the idea of a border poll when questioned about political matters in Northern Ireland.
The Stormont Assembly has been collapsed amid DUP protest action against internal UK trade barriers created by Brexit’s Northern Ireland Protocol.
The DUP has made clear it will not accept a return to devolution until the UK Government provides further assurances, by way of legislation, over Northern Ireland’s place in the UK internal market.
In June, Mr Varadkar said that Irish unification could fall off the agenda for a long time if a border poll was held and defeated.
Sir Keir, speaking to BBC News NI ahead of the Labour Party conference in Liverpool, said: “I don’t think we’re anywhere near that kind of question.
“It’s absolutely hypothetical.
“It’s not even on the horizon.”
“Our rules must be made in Westminster, according to the national interest of the UK as a whole.
“I am interested in resolving some of the outstanding issues.
“And obviously, that will mean making progress on things like the Windsor (Framework) agreement, the protocol, because that was a step in the right direction, which is why we said we would support it.
“So it’s quite clear that there can be improvements and I think in Northern Ireland in particular, there will be a lot of interest in whether we cannot have some measures which take away some of these still remaining tensions that are very obviously there.”
Sir Keir’s comments on Thursday came as Prime Minister Rishi Sunak held talks with Mr Varadkar at the European Political Community summit in Spain.
A No 10 spokesperson said: “The Prime Minister and Taoiseach shared their concerns about the continued absence of an executive in Northern Ireland and the democratic deficit this was causing.
“The Prime Minister set out the steps the UK is taking to ensure a return to powersharing and the two agreed to stay in close contact in the coming weeks.
“The two leaders also touched on their respective positions on the issue of legacy and agreed that teams should continue to stay in touch.
“The leaders also discussed a wider set of issues, including support for Ukraine and bilateral cooperation on security and migration.
“They also welcomed the recent UK-Ireland agreement on energy as a sign of the good working relationship between the two governments.
“The leaders noted the progress of the UK and Ireland’s historic joint bid to host Euros 2028.
“They talked about the potential of using the occasion to strengthen bilateral ties and leave a positive legacy in communities, including for grassroots football in Northern Ireland and elsewhere.”