Boris Johnson must table written proposals within a week to fix “gaping holes” in his plans for the Irish border, the EU has said, as a former Irish taoiseach cited the IRA’s attempt to kill Margaret Thatcher as the violence he risked fuelling.

EU diplomats briefed by the European commission on the latest proposals from London, including a fourth confidential paper, suggested it would take a miracle for there to be a meeting of minds before a crunch summit on 17 October.

The UK’s latest paper builds on a model of checks and controls on goods entering and being traded around Northern Ireland and the Republic of Ireland that the EU says will be a boon to smugglers, and rely on systems that do not yet exist.

The former Irish taoiseach John Bruton suggested Johnson appeared happy to offer “an open invitation to criminal and subversive organisations who have financed themselves in the past by smuggling”.

“Given that one such smuggling-financed criminal organisation attempted to murder one of Mr Johnson’s predecessors as leader of the Conservative party, one would be forgiven for thinking that he has not studied the history of his party as closely as he should have done,” he said.

The IRA attempted to kill Thatcher in a bomb attack at the Grand hotel in Brighton on the first day of the Conservative party conference in 1984. Johnson is due to appear at the Tory conference in Manchester this weekend.

Revealing details of his conversation with the head of the European council, Donald Tusk, in New York during the UN general assembly, the current Irish taoiseach, Leo Varadkar, offered his own downbeat analysis as he set Downing Street its deadline.

Varadkar said: “We have working methods and I know that President Tusk and other EU heads of government would like to see British proposals in writing really in the first week of October, otherwise it is very hard to see how we could agree something at the summit in the middle of October.

“The withdrawal agreement is actually an international treaty. It’s not the kind of thing that can be amended or cobbled together late at night at the European council meeting on 17 October.

“So if the UK does have meaningful proposals, changes that they would like to suggest to the withdrawal agreement or to the joint political declaration more particularly, we really need to see them in advance so that they can be worked through and worked up in advance of the EU summit.”

Q&A What is a Northern Ireland-only backstop? Show The British government’s version of Brexit involves the UK ultimately leaving the single market and customs union, requiring the return of a range of checks on goods crossing the border between Northern Ireland and the Republic of Ireland. The “backstop” is intended as a standstill placeholder to ensure such checks do not have to be imposed between Brexit happening with a deal, and the start of a new free trade agreement yet to be negotiated between the UK and the EU. Theresa May's withdrawal agreement proposed keeping the whole of the UK in a shared customs territory with the EU during this period. An alternative idea involves only Northern Ireland staying in the EU’s customs territory. That would place a customs border in the Irish Sea. May described it as a threat to the constitutional integrity of the UK, but the new prime minister, Boris Johnson, has opened the current talks by proposing an all-Ireland agri-food zone. The suggestion is that he will seek to quietly build on that with further NI-only arrangements. Given an NI-only backstop was an EU proposal in the first place, the U-turn would be warmly welcomed in Brussels, although attempts to give the Northern Ireland assembly a veto on its continuation would not be acceptable, and the DUP would be unlikely to support the prime minister in such a move in parliament. If there is a no-deal Brexit, then there is no backstop. Daniel Boffey

Officially, the EU still maintains that the withdrawal agreement cannot be reopened, but Varadkar’s comments, taken in conjunction with other remarks made in recent days, indicate a softening of this hard line.

Talks between UK officials and the commission continued in Brussels on Wednesday but EU diplomats said they could see little cause for optimism. Johnson’s chief negotiator, David Frost, was not in attendance.

“I suppose they will keep on turning up and we will continue to engage but even trying to gather what the UK wants to talk about in these talks is difficult – even that needs political signoff and it seems difficult to get,” said one EU source.

“People have been saying for ages that we might have to wait until after the Conservative party conference for new proposals – but, really, will it make a difference? The gap between the two sides is so large. And it is just weeks now until the summit. It seems certain that the UK will seek an extension, and there isn’t a majority for a deal in parliament.”

The European parliament’s Brexit co-ordinator, Guy Verhofstadt, said the EU had not received any alternatives to the backstop which were deemed acceptable by the EU. “We cannot say that legally operative alternatives have been put on the table,” he said, reiterating comments made by the chief Brexit negotiator, Michel Barnier, in recent days.

The British discussion papers – on a single agri-food zone for the island of Ireland, a customs border on the island of Ireland, a model of light-touch market surveillance for standard compliance in manufactured goods and the range of intelligence-led checks at airports on food imports – were “only potential components of an alternative”, Verhofstadt said.

“Needless to say that the risks to the single market under this proposal are as big as the risks to the stability of Northern Ireland by a diverging regulatory makeup,” said one EU source.