Stormont talks: Theresa May in Northern Ireland on Monday, when she and Leo Varadkar discussed the state of play in Brexit talks. Photograph: Niall Carson/PA Wire

Ms May said the deal would ensure “no hard border” in Ireland and added the deal was a “significant improvement” which had required give and take on both sides.

The British prime minister, Theresa May, asked Taoiseach Leo Varadkar to help explore how to shape the UK’s future relationship with the European Union without invoking a default arrangement that would keep Northern Ireland closely aligned with EU rules.

The British government is understood to be concerned about an emerging focus on the clause in a pre-Christmas deal that includes a commitment to avoiding a hard Border in a so-called no-deal scenario.

Informed sources said this concern informed the discussion between the two leaders when they met in Belfast earlier this week, with London believing more consideration should be given to alternative solutions.

The clause outlined in the pre-Christmas deal, which allowed the Brexit talks to proceed to the next phase, focusing on the post-Brexit transition deal, said that in the absence of an EU-UK trade deal Northern Ireland would maintain “full alignment” with the European single market and customs union.

This would apply only if there were no overarching EU-UK deal that would avoid a hard border, or no agreement on specific solutions that the UK would provide to avoid a hard border. Sources said the British government is still raising the prospect of technological solutions.

Deal to prevent hard border Ms May, according to sources, asked Mr Varadkar that the Government allow officials to begin to flesh out how an overarching deal could prevent a hard border. Mr Varadkar is understood to have agreed, but he also said that the British government needs to make a political decision on what shape its future relationship with the EU will take.

Numerous government sources said that it is extremely difficult to envisage an outcome that will avoid a border if Britain insists on leaving the single market and customs union, as Ms May has promised.

It is also insisted that Ireland will negotiate with the UK under the auspices of the EU task force representing all member states. But sources disclosed that bilateral discussions could take place on issues of exclusive concern to Ireland and the UK, such as the Common Travel Area and the Border.

Ireland is insisting that this commitment be translated into a firm legal text and followed through if the Government is to agree to Ms May’s request to explore her favoured options. “They want to be able to focus on solving the Border issue through a broad future-relationship agreement,” said a source.