There will be no three-way talks about the Irish Border between the UK, Ireland the European Commission, the Taoiseach has said, rejecting an apparent suggestion from British prime minister Theresa May in a major Brexit speech last week.

Ms May said she and Leo Varadkar had agreed “that our teams and the commission” should work together to find a solution to the future of the Border once the UK leaves the European customs union.

However, Mr Varadkar on Monday said there would be no three-way negotiations. “There won’t be tripartite or three-way talks. What will happen is there will be talks between the EU 27 and the UK. Ireland is part of the EU 27 and we’re much stronger as one of 27,” he told RTÉ’s Morning Ireland.

The Taoiseach said there would be consultations with the UK about issues such as the Common Travel Area between Ireland and the UK.

“That’s a bilateral arrangement, it makes sense that we talk about those things and we will of course have consultations about what could be done to avoid a hard border,” he said.

“But what we won’t be getting into is a negotiation with the UK or a three-way negotiation. That’s not in our interest, and not the way that this can be concluded. Ultimately this is going to be a set of treaties between the EU and the UK to define the new relationship.”

A spokesman for Mr Varadkar later confirmed that it was the Government’s position that there could be “no formal bilateral component” to the discussions on the Border.

“Everything will be done with the [EU]task force,” he said.

‘Cake and eat it’

Otherwise, Mr Varadkar gave Ms May’s speech “a guarded welcome”.

“In terms of what was new, there was recognition that the UK might have to give some things up, that there isn’t going to be a cake and eat it, that they would have to give up financial passporting for example, that’s the first step to realising and preparing the British public for a lot of the downsides of Brexit, there was a little bit more flesh on the bones of how a Customs Agreement might work,” he said.

“But it’s still not nearly enough 20 months after a referendum. What I would say is I am reassured by her commitment to there not being a hard border, her commitment to the Good Friday Agreement which some people have been questioning, and also the transition period.

“But we’re still not where we should be.

“It’s really only a year and a bit away now. If we’re going to conclude an agreement by October I think we’re going to see a lot more detail from the UK government. What we want is not so much principles and aspirations and red lines. What we want is detail written down in black and white that can be codified and put into law.”