Boris Johnson has been accused of “gaslighting” voters over the prospects of a Brexit deal after EU sources said the prime minister brought nothing new to his first meeting with European Council president Donald Tusk.

In public, Mr Johnson said that the chances were “improving” of a fresh agreement on the terms of the UK’s departure ahead of the 31 October deadline for Brexit, although he conceded that it remained “touch and go” whether a deal would in fact be reached.

But a senior EU diplomat said that Mr Tusk was none the wiser after their 20-minute meeting at the G7 summit in Biarritz on the alternative arrangements Mr Johnson envisages for the Irish border to avoid the need for the disputed backstop.

And it emerged that Mr Johnson did not even mention the issue of the UK’s £39bn financial settlement, despite briefings that he would use the threat that as much as £30bn of the sum agreed by Theresa May could be withheld in a no-deal situation as leverage to encourage the EU to make concessions. In TV interviews, the PM said that “very substantial sums” could be redirected to domestic priorities if no agreement is reached.

Meanwhile, the prime minister raised hopes of a free trade deal with the US within a year after talks with Donald Trump during which the president hailed the PM as “the right man for the job” of delivering Brexit.

Mr Johnson declined to give a predicted date for the conclusion of negotiations on thorny issues such as access for US chlorine-washed chicken and GM crops to the UK market, but said that suggestions it would take years were “an exaggeration”.

“The Americans are very ambitious to get this done as fast as possible,” he said. “They really want results within a year – I suppose by next June or July. We’re keen to go as fast as we can. But we want this to be a really big thorough comprehensive trade deal.”

Mr Johnson and Mr Tusk are not scheduled to meet again until the UN general assembly in New York in the last week of September – which comes after the end of the 30-day period within which German chancellor Angela Merkel has suggested Mr Johnson should set out his proposals.

The EU diplomat said there was “no detailed discussion at all” and “no new substantive efforts from any side” during the Biarritz meeting, adding: “The ball is really squarely and firmly in the UK court. They have been telling the press they have new ideas and eventually they will come up. But they didn’t come up today.”

Underlining EU27 scepticism over UK claims to have viable proposals for the Irish border, the official added: “The brutal fact is that there is nothing. Alternative arrangements have always been part of the agreement – but we still don’t know what they look like.”

Speaking ahead of the meeting in the French beach resort, Mr Johnson said he had detected a “change in mood” in the EU and was hopeful of starting fresh Brexit talks “in the coming weeks”.

Mr Tusk said he was open to “serious talks” on any UK ideas that were “operational, realistic and acceptable to all member states, including Ireland”.

But the two men also made clear their readiness to point the finger of blame at the other for any lack of progress, with each warning the other he risked going down as “Mr no deal”.

Asked what the likelihood was of a deal by Halloween, Mr Johnson said: “It all depends on our EU friends and partners. It depends very much on the willingness to cooperate and the Commons.

“I do think they understand there’s an opportunity to do a deal. I think it’s going to be touch and go.”

The PM was asked whether he could promise there would not be medicine and food shortages after 31 October if there is no deal.

“What I can tell people and as I said a few weeks ago on the steps of Downing Street, I think we can get through this, this is a great, great country the UK, we can easily cope with a no-deal scenario. And I know that's what people want,” he said.

“Frankly I think it’s highly unlikely that there will be food shortages of any kind.”

Having starting his day with a dip in the Atlantic before his breakfast talks with Mr Trump, Mr Johnson said his swim offered a metaphor for the state of Brexit talks.

Boris Johnson arrives at G7 summit in Biarritz

“I swam round that rock this morning,” he said. “From here you cannot tell there is a gigantic hole in that rock. There is a way through.

“My point to the EU is that there is a way through, but you can’t find the way through if you just sit on the beach.”

Referring to a popular term for a false impression about the reality of a situation, Labour MP Alex Sobel said that Mr Johnson’s “willingness to gaslight the British public seems to have no limits”.

Mr Sobel, a leading supporter of the People’s Vote campaign for a second EU referendum, said: “Recently, Boris Johnson was claiming that the chance of crashing out of the EU in a disastrous no deal was ‘a million to one’ but just a few weeks later it’s “touch and go”.