The French government has threatened to veto a further Brexit extension due to the “worrying” lack of progress in the recent talks, as EU diplomats expressed their frustration at being caught up in game-playing by the British government.

In a sign of rising exasperation, the French foreign minister, Jean-Yves Le Drian, highlighted the lack of realistic proposals being put forward by Downing Street as an alternative to the Irish backstop.

“It’s very worrying. The British must tell us what they want,” Le Drian said.

When asked if an extension beyond 31 October was possible, Le Drian said the EU’s patience was waning. “We are not going to do this [extend the deadline] every three months,” the French minister added. The Benn bill, due to receive royal assent this week, would extend the UK’s membership until 31 January 2020.

The UK government wants to remove the Irish backstop, which would keep Northern Ireland in the single market and the UK in a customs union to avoid a hard border on the island of Ireland.

But sources in Brussels, where Boris Johnson’s envoy, David Frost, has been in twice-weekly talks with the European commission’s Brexit taskforce, said the process of finding a ready alternative was proving to be “a farce”.

“There have been no substantive proposals on how to replace the backstop and the British are pretending otherwise – we are being instrumentalised for domestic purposes,” said one diplomat.

EU sources have said there is no evidence the British government is even working on “concrete proposals” to strike a Brexit deal, and the latest resignations from the government, recent reports of “sham negotiations” and constant election talk have all contributed to the impression that the government is not serious about finding an agreement.

The comments appear to confirm the fears of the former work and pensions secretary Amber Rudd, who resigned on Saturday, citing the lack of effort being put into negotiating a deal.

On Friday, Frost proposed to hold discussions over an all-Ireland agri-food zone, which Johnson has said may offer a “germ” of a solution to the current Brexit impasse.

The EU insists that such a concept on its own falls far short of honouring the commitments made by the British government to maintain the all-Ireland economy after Brexit and avoid checks on all goods passing between Northern Ireland and the Republic of Ireland.

“We have the Brits ringing up saying: ‘It’s great that we are going to work on this agri-food zone idea,’ but it just feels like a distraction from all the other problems that need solving,” a source said.

Of the last meeting with Frost, the diplomat added: “No proposals on the idea itself were received and therefore discussed.”

In Brussels, the absence of papers is seen as a sign that the UK is not serious about finding an agreement. British officials reject this criticism: the UK has not put pen to paper because ministers are worried the EU will immediately shoot down proposals. The UK would like Brussels to share the task of finding an alternative to the backstop.

An EU diplomat said that “given the present stance of No 10 and the apparent lack of concrete and implementable UK proposals to substitute the backstop, frustration is growing rapidly among the EU27”.

That exasperation has been further fuelled by the decision to pull UK officials out of some EU meetings as part of what Johnson has described as an “unshackling” from the bloc.

“They have taken people out of these meetings so they can work on no deal, but then they have to ring round the member states begging for reports of what is being discussed,” complained one EU diplomat. “It just becomes more ridiculous by the day.”

The threats by the UK government as it battles with parliament over an extension beyond 31 October could further poison relations when the British government is seeking concessions in Brussels.

Downing Street officials have suggested that if Johnson were forced to extend the UK’s membership of the EU he would not nominate a European commissioner, which would leave the bloc’s institutions in limbo and unable to work. Sources have suggested that this threat would be enough to dissuade the EU from agreeing to an extension.

A former director general of the EU council’s legal services, Jean-Claude Piris, said the UK gambit was based on a misunderstanding.

He said: “The commission will be legally able to function and take legal decisions with a member less. If the UK is still an EU member it is that member state which would violate the treaty and could be brought to the EU court of justice.

“The EU parliament will not find that the commission will not be legally constituted. The commission has already functioned during a period with a number of members inferior to the number set up by the treaty.”

The French foreign minister’s threat of blocking an extension will be seen as an expression of heightened irritation but EU sources have suggested it is unlikely to come to pass.

EU leaders have said a second referendum or general election would be sufficient reason to extend again and, for all the frustration at the British, there is a reluctance to appear to be pushing the UK out of the bloc.

The European commission president, Jean-Claude Juncker, has repeatedly said a no-deal Brexit would never be an EU choice.