Published: 9:50 AM April 18, 2018 Updated: 8:42 AM September 18, 2020

The European Union has issued a fresh warning to the UK that a transitional deal after Brexit will not be secured unless the problem of the Irish border is resolved.

European Council president Donald Tusk told MEPs that the UK had created the issue as a result of the Brexit vote and had a duty to find a solution.

His comments came as Theresa May faced a battle in the House of Lords, with peers set to push for the UK to remain in a customs union after leaving the EU - something which they claim could help address the issues around the border between Northern Ireland and the Republic.

The prime minister hopes to secure a transitional deal which would see the UK continue to follow EU rules and trade with the bloc on similar terms until the end of 2020, when a comprehensive deal on a new partnership could take over.

Speaking at the European Parliament in Strasbourg, Mr Tusk said he welcomed the progress that had been made in the Brexit talks.

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"We want to use the positive momentum in these negotiations to finally settle outstanding issues, such as the solution to avoid a hard border between Ireland and Nothern Ireland," he said.

In a message that the government could not simply leave it to the Irish and EU to decide what the customs arrangements at the border should be - as some Brexiteers have suggested - Mr Tusk said: "The UK's decision on Brexit has caused the problem and the UK will have to help solve it.

"Without a solution, there will be no withdrawal agreement and no transition.

"Leaders will assess the negotiations in June. In parallel we will start our first talks about the future EU-UK relationship."

Senior officials are meeting in Brussels today to hold preliminary discussions about the future relationship for the first time.

In Westminster, the prime minister faces the prospect of defeat at the hands of a cross-party alliance in the Lords.

The upper chamber resumes debate on the government's flagship Brexit legislation on Wednesday with an alliance of Labour, Liberal Democrat and crossbench peers - along with Tory rebels - eager to soften the prime minister's approach.

Labour has warned that opposition peers "won't be shy" about inflicting defeats in the House of Lords.

Attempts to rewrite the European Union (Withdrawal Bill) include a cross-party amendment which would require ministers to negotiate "an arrangement which enables the UK to continue participating in a customs union with the EU" after Brexit.

The amendment's sponsors include former Tory party chairman Lord Patten of Barnes and former UK ambassador to the EU Lord Kerr of Kinlochard - the diplomat who drafted Article 50, the legal mechanism for Brexit.

Former UK ambassador to France and national security adviser Lord Ricketts said he would also back the amendment.

Shadow Brexit minister Baroness Hayter said the proposed change "forces the government to prioritise a customs union with the EU - not only to boost industry's ability to trade with the UK, but to ensure there is no hard border in Northern Ireland".

Downing Street maintained its opposition to a customs union, which would restrict the UK's ability to strike trade deals after Brexit.

The prime minister's official spokesman said Mrs May "has been very clear that the British people voted to leave the EU and expect us to be able to sign trade deals around the world, operating our own independent trade policy".

"As the PM has set out, that means we are leaving the customs union," the spokesman said.

The government could try to overturn any defeats inflicted in the Lords when the Bill returns to the Commons later this year.

The latest Brexit skirmishes come as a report by think tank Global Future - which wants a Britain that "reaches out to the world" - claimed the prime minister's hoped-for bespoke deal would cost the UK the equivalent of £615m a week in 2018 prices.

The think tank said each of the four possible Brexit options - European Economic Area membership, a Canadian-style free-trade deal, falling back to World Trade Organisation terms, or the comprehensive partnership sought by the prime minister - would leave the UK poorer than it otherwise would have been.

In the report, economist Jonathan Portes said: "In today's money, the government's estimates imply a cost of about £260m a week, or 9% of what we currently spend on the NHS, for the EEA option; £875m per week, or 30% of what we currently spend on the NHS, for the Canada option; and a whopping £1.25bn a week, or about 44% of what we currently spend on the NHS, for the WTO option.

"The prime minister's recent Mansion House speech, setting out in detail what the government means by a 'bespoke deal', allows us to make a reasonable and credible estimate of what the same methodology yields for the government's bespoke deal - a cost of about £615m a week, or 22% of what we spend on the NHS.

"If we are to decide what sort of Brexit we want, the least we need is a menu, with prices."