At this week’s summit of heads of government, the European Union and the United Kingdom are likely to agree on a transition period and a timetable for talks on the outline of the future trade deal. In the autumn, the two sides will probably finalise the text of the withdrawal agreement, enabling the UK to leave the EU at the end of March 2019. However, the issue of the Irish border remains unresolved, and could still wreck the Brexit talks. Despite warm words in the run-up to the summit, the British and Irish positions appear fundamentally incompatible.

The UK government plans to leave the single market and the customs union. It says it wants to avoid a hard border on the island of Ireland. But some in Ireland doubt its sincerity: the British know the EU will need to police its single market and customs union by checking for compliance with its standards for industrial and agricultural goods, as well as tariffs and rules of origin. So how could a hard border be avoided?

The joint report signed by the EU and the UK in December sketched out three possible answers. Option A would sort out the border as part of the overall EU-UK agreement on future relations. Option B would be Ireland-specific solutions based on advanced technology. And if neither A nor B proved viable, option C would apply: in the north there would be “full alignment” with those EU rules required to support the Good Friday agreement and north-south cooperation. The joint report also ruled out – to placate the Democratic Unionist party – new barriers between Northern Ireland and Britain.

The British reckoned that C meant aligning just some rules, while the Irish and the EU thought it meant much more. To remove the ambiguity, the commission spelled out the precise meaning of alignment in the Irish protocol of the draft withdrawal agreement, published last month. This would keep Northern Ireland in the customs union and the single market for goods and electricity, and abiding by EU rules on plant and animal health, VAT and state aid. Northern Ireland would be subject to the European court of justice. The protocol said nothing about excluding a border in the Irish Sea.

The British government was flabbergasted, believing the spirit of the Good Friday agreement – that both communities in Northern Ireland should agree to constitutional arrangements – had been flouted. Even some of the most pro-EU cabinet ministers were perturbed, worrying about the impact on public opinion of an apparent attempt by the EU to impose its rules on Northern Ireland. Theresa May said that no British prime minister could accept the wording of the protocol. But there was not much sympathy for the UK among EU governments. They thought the protocol’s firm line was required to prevent the UK backsliding on its commitments.

The EU has not made agreement on the transition conditional on the UK signing the protocol. But it has insisted that the UK state that it accepts that the withdrawal agreement should include a “legally operative version of the ‘backstop’ [option C] … in the joint report”, and that this will apply unless another solution is found. The UK has also agreed to tackle the border through a new trilateral negotiating process with the commission and Ireland. But all this merely postpones rather than resolves the border problem, which may blow up at June’s EU summit. The Dublin government is adamant that it will not accept any infrastructure on the border lest it become a target for terrorists. It does not believe that option B, clever technology, is viable. Asked how option A could work, it says the UK would have to stay in the single market and the customs union – which May rejects. Hence the importance of option C for the Irish. But the draft protocol’s version of that option remains unacceptable to May and the DUP.

The 26 other EU governments say they are right behind Ireland, but are they? In private, if not in public, some of them hope for a compromise. Their diplomats, like some senior EU officials, believe that if the UK leaves the customs union and the single market, controls of some sort will be necessary.

If the Irish really tried to make May swallow the protocol as it stands, there would be no deal

“We need local solutions that ensure checks can be carried out, in a way that avoids the need for a hard border,” said one official. “The checks would be near the border but not on it,” said another. Some French officials think option B is the best way forward.

However, the UK cannot count on the member states cajoling Ireland to climb down. Even those governments that hope for compromise say that if Dublin calls on their support, they will stand by it.

Some UK officials want to mix options A, B and C. They talk of a “customs partnership”, whereby the UK would police the EU’s customs union on its behalf and vice versa, obviating the need for border checks. But the EU says this is “magical thinking”, and unrealistic. British officials think option B could help solve the border problem, with methods such as number-plate recognition, electronic pre-clearance and trusted-trader schemes. They also think the less sensitive parts of option C, such as aligning with EU rules on plant and animal health, would help. In addition, they would let small traders cross the border unhindered.

All that could reduce, but probably not eliminate, the need for some checks near the border. Could the Irish live with that? They say not. But if they really tried to make May swallow the protocol as it stands, there would be no deal. And that would damage the Irish economy almost as much as that of Britain. Several of Ireland’s EU partners will gently encourage the Irish to accept a less than perfect outcome on the border.

• Charles Grant is director of the Centre for European Reform