Taoiseach Leo Varadkar looks on at a Fine Gael party event pressing for a 'Yes' vote in the upcoming May 25th referendum on abortion law, in Dublin, Ireland, April 21, 2018. REUTERS/Clodagh Kilcoyne

LEUVEN, Belgium (Reuters) - Britain and European Union negotiators must make further progress on the issue of the Irish border by June if talks are to move forward on a final withdrawal agreement, Irish Prime Minister Leo Varadkar said on Thursday.

Northern Ireland will be the UK’s only land frontier with the EU after its leaves the bloc. Both sides say they are committed to keeping the border with Ireland open, but finding practical solution has proved elusive so far.

Britain says an EU-UK free-trade deal to be sealed by 2021 can do that. Dublin insists the Brexit treaty must lock in a “backstop” arrangement in case that future pact does not work, something London signed up to achieving last month.

“We want to see further progress in June, and if we’re not making further progress, then we have to ask serious questions as to whether there can be a withdrawal agreement at all,” Varadkar told reporters in the Belgian city of Leuven.

“I’m optimistic that further progress can be achieved before the June (European) Council ... So far, the British government hasn’t managed to write down an alternative that we believe works, but there is time between now and June for that to be done. There’s still a lot of work to do.”

British Brexit Secretary David Davis said on Wednesday that he regarded June as an “artificial deadline” before the crunch period in October when EU negotiators say the withdrawal agreement must be ready to allow time for ratification.

After British lawmakers stepped up pressure on Prime Minister Theresa May over her Brexit strategy on Thursday, criticising her refusal to pursue a customs union with the EU, Varadkar again urged London to change tack if it wants to secure a close relationship with the EU after Brexit.

“The biggest barrier to that at the moment is the very, very hard red lines that the UK government has set down. If there is a softening of those red lines, there is also the ability of the European Union to meet the United Kingdom halfway and soften its positions as well,” he said.