Michel Barnier has claimed a Brexit deal could be within reach by next Wednesday but warned the prime minister that only by abandoning a key red line and agreeing to a customs union can impediments on trade between Northern Ireland and the rest of the UK be avoided.

The British government would have to give up on its plans for free-trade deals with China and the US under such an agreement, the EU’s chief negotiator insisted, but otherwise a customs and regulatory border within the territory of the UK will have to be erected.

The EU’s contentious proposal for avoiding a hard border on the island of Ireland after Brexit is for Northern Ireland to, in effect, stay in the customs union and remain under single market regulations, while the rest of the UK withdraws.

In a speech in Brussels, Barnier reiterated his rejection of the counter-proposals hammered out by the cabinet at Chequers, which Theresa May insists is the only deal that respects both the referendum result and the constitutional integrity of the UK by ensuring “frictionless” trade and no hard border.

The prime minister’s plan for a common rulebook on goods and a customs arrangement that meant the UK could avoid border checks, while allowing the country to sign its own bespoke trade deals, would give British companies “a huge competitive edge” and be “counter to our very foundations”, Barnier said.

He instead encouraged Britain to make a final push in the talks, offering to launch “around 10 negotiations running in parallel” from April 2019 on an EU-UK trade deal, if agreement can be found now on the Irish border issue and the principles of a Canada-style free trade deal.

If the prime minister did not opt for the whole of the UK staying in a customs union, Barnier insisted that Northern Ireland would under the EU’s proposals gain an unprecedented advantage in enjoying the benefits of the single market and the EU’s future free trade deals, unlike the rest of the UK.

Barnier said that he recognised that treating Northern Ireland differently to the rest of the UK was “politically sensitive”. The Democratic Unionist party has said it will withdraw its support for May’s government and vote down such a deal, and even the coming budget, if it were agreed by the prime minister.

The European commission official conceded that the EU plan for the province would involve “administrative procedures that do not exist today for goods travelling to the Northern Ireland from rest of the UK”, with checks on live animals increasing tenfold.

But, “Brexit was not our choice”, Barnier said. “Our proposal tries to help the UK in managing the negative fallout of Brexit in Northern Ireland in a way that respects the integrity of the UK”.

He added: “Our proposal is just a safety net, the backstop. It is needed because the detail of the future withdrawal with the UK will only begin after the UK withdraws.

“The future relationship itself might mitigate the checks and even make some unnecessary. For instance a veterinary agreement between the EU and the UK would mean less frequent inspections of live animals … And we are still open – we are still open – to the idea of having a customs union with the UK. Such a customs union would eliminate an important part of customs checks.”

The former French minister said the principles of the joint political declaration on a “free trade area”, which needs to be agreed within the coming weeks along with the main withdrawal agreement on key topics, including the Irish border, could be “enriched” once talks on a trade deal start in earnest after Brexit day on 29 March, should the UK’s red lines evolve.

An EU leaders summit, known as a European council, starting next Wednesday has been described by Donald Tusk, the president of the European council, as a “moment of truth” at which “maximum progress” needs to be seen.

Barnier said: “Negotiations with the UK continue this week intensively, day and night, in the goal set by the leaders of the 27 that the agreement is ‘in reach’ at the time of the European Council of 17 October, next Wednesday”.

The latest intense round of negotiations are being described in Brussels as “the tunnel”, with both sides reluctant to divulge details in a sign of the high stakes and heightened sensitivity around the talks.

Barnier had updated European commissioners in Brussels on the talks earlier on Wednesday. “Michel Barnier and his team are working day and night to reach a deal, but we are not there yet,” said Dimitris Avramopoulos, the European commissioner for home affairs and migration, who heard the briefing.

The commissioners also had an update on the EU’s no-deal plans from the powerful secretary general, Martin Selmayr. Officials had cancelled the publication of a no-deal paper planned for Wednesday, fearing it would upset negotiations at a delicate moment.

Avramopoulos offered an upbeat message, as he declined to elaborate on no-deal plans in his area. “Our plans are defined by our goodwill to continue our cooperation in the future in the field of information exchange, intelligence exchange and of course deepen even more our trust.