The European Commission’s negotiators have cast doubt on Theresa May’s ability to take the UK out of the single market and customs union if she follows through on her solution to the Northern Ireland border issue.

An internal EU communiqué from its negotiators to the EU27 member states of the European Council says it is difficult to see how Ms May could still be planning on leaving the two institutions given what she agreed in the early hours of this morning.

The Prime Minister told reporters in Brussels this morning that Britain would still be leaving the single market and customs union, as she had pledged in her Lancaster House speech at the start of the year.

But the joint text she signed up to just minutes earlier pledged that the entire UK would “maintain full alignment with those rules of the Internal Market and the Customs Union” where they were applicable to avoiding a hard border on the island of Ireland.

The communication from the Commission to the Council, issued later on Friday after the PM had returned to the UK, says EU negotiators believe it will be difficult to follow through on this commitment without keeping the UK in the single market and customs union.

“Whilst the United Kingdom remains committed to protecting and supporting continued North-South cooperation across the full range of contexts and frameworks, including after withdrawal, the common understanding provides that the United Kingdom aims to achieve this protection and the avoidance of a hard border through the overall EU-United Kingdom relationship,” the 2,600 word communication says.

“This intention seems hard to reconcile with the United Kingdom’s communicated decision to leave the internal market and the customs union.”

Despite the Commission’s suggestion, a Downing Street spokesperson echoed Theresa May, telling reporters in Westminster: “We are leaving the single market and customs union. I’ll write it on a sign.”

The Government has offered no detailed explanation of how it could simultaneously leave the single market and customs union and also sign up to rules to prevent a hard border in Northern Ireland, however.

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The PM’s deal on Northern Ireland is the final piece in the jigsaw required for her to progress to the next round of Brexit talks, for which she is expected to get the green light at a Brussels summit next week.