Jeremy Corbyn has accused Theresa May of closing down solutions to the Brexit impasse by refusing to countenance customs union membership or to rule out no deal, saying these could command majority support in the Commons.

Again using all his time at prime minister’s questions to focus on the stalled Brexit strategy, Corbyn argued that May’s promise to liaise with other parties was meaningless if she declined to abandon any of her red lines.

“It appears that while the door to her office may be open, apparently the minds inside it are completely closed,” the Labour leader said, borrowing a line used by one of his MPs, Hilary Benn, earlier in the week.

In response, May lambasted Corbyn for being the only opposition party leader to refuse to discuss Brexit with her in person, and mocked his demand for a future customs union with the EU as vague.

Before a slightly subdued Commons, which has witnessed similar exchanges numerous times in recent weeks, Corbyn began by noting reported comments from the chancellor, Philip Hammond, to business leaders, reassuring them a no-deal departure would not happen.

“So will the prime minister listen to her own cabinet members and take no deal off the table?” Corbyn asked.

After arguing that the only way to rule out no deal was to pass her deal, May queried Corbyn’s decision to not join her for discussions: “The right honourable gentleman has been willing to sit down with Hamas, Hezbollah and the IRA without preconditions, yet he won’t meet me to talk about Brexit.”

Corbyn replied: “The only consistency in her strategy seems to be running down the clock on this by threatening no deal as an alternative to her dead deal.”

Jeremy Corbyn, who the prime minister claimed ‘hasn’t got a clue’. Photograph: Andy Rain/EPA

In later exchanges about a post-Brexit customs union, which Labour wants, May declined explicitly to rule this out, but mainly because she answered Corbyn’s question by mocking what he said was Labour’s vagueness as to the details of this.

“If he won’t talk about it there’s only one conclusion: he hasn’t got a clue,” she said. May added later: “The right honourable gentleman is doing what he always does: he just stands up, uses these phrases, and the honest answer is I don’t think he knows what those phrases mean or what the implications of those phrases are.”

Corbyn said the government was in chaos over Brexit, highlighting the previous promise by Liam Fox, the international trade secretary, that dozens of new trade agreements would be in place “the second after Brexit”.

He said: “Why is the prime minister prepared to sell people’s jobs and living standards down the river rather than negotiate a customs union that would be part of a sensible deal for the future?

“While a third of her government are at the billionaires’ jamboree in Davos, she says she’s listening, but rules out changes on the two issues where there might be a majority – against no deal, and for a customs union, part of Labour’s sensible alternative.

“If the prime minister is serious about finding a solution, which of her red lines is she prepared to abandon? Could she name a single one?”

May replied: “He makes claims about minds being closed; he asks about red lines. Why doesn’t he just come and talk about it?”