Parliament can stop the UK leaving the EU without negotiating a deal, shadow chancellor John McDonnell has said.
There was not a Commons majority for such an outcome, he told the BBC, and Labour would work with other parties to stop the "damage" it would cause.
He urged ministers to "come to their senses" and publish legal advice about what was owed in financial liabilities.
Transport Secretary Chris Grayling said the UK will "succeed come what may" but he was confident of a "sensible deal".
Dismissing Mr McDonnell's comments as "complete nonsense", he told the Andrew Marr show on BBC One that it was a "legal reality" that the UK would be leaving at the end of March 2019 after Article 50 was triggered earlier this year.
Meanwhile, Brexit minister Robin Walker has suggested the three million citizens of other EU countries currently living in the UK will be able to stay regardless of the outcome of the negotiations, telling Pienaar's Politics on BBC Radio 5 live "yes, people will be allowed to stay".
Prime Minister Theresa May has said she believes the two sides will reach a deal but the UK must prepare for all eventualities.
As it stands, the UK will leave the EU in March 2019 whether it agrees a deal on the terms of withdrawal or not.
But Mr McDonnell said he could "not countenance" such a situation and Parliament had the power to force the government to conceded a "meaningful vote" on the terms of exit, by amending the EU Withdrawal Bill or other relevant legislation related to Brexit.
"I don't think no deal is a realistic option," he said. "There are enough sensible people in the House of Commons to say 'this cannot happen, we cannot damage our country in this way'."
Urging ministers to stop "fighting" among themselves and focus on what was best for the economy, he added: "They should come to their senses, behave responsibly and look after the interests of the country."
He called on ministers to publish legal advice about the size of the so-called divorce bill, saying the UK should honour its obligations but the final figure should not be anywhere near the £60bn quoted in some quarters.
The government has appointed a Brexit "contingency minister" and will spend £250m this year on preparing for the UK's exit, including the possibility of it leaving without an official deal.
Speaking on the same programme, Mr Grayling said talks were always going to be "long and challenging" and it was fanciful to suggest the two sides would "shake hands and do a deal in half an hour".
While he believed that the two sides would ultimately reach agreement, he said Labour was wrong to argue for a deal in any circumstances and he was not personally afraid of the UK leaving the EU without one.
"Britain will succeed come what may but I don't think we will come to that. I think we will agree a sensible trading partnership... because it is in both of our interests for this to happen."
He rejected suggestions that flights would be grounded - as one major airline has suggested - in the event of a no-deal Brexit, insisting "people will be able to carry on making their bookings".
Asked about reported cabinet divisions, Mr Grayling said ministers were "not clones" but there was a spirit of collaboration and Philip Hammond, criticised in recent days for being too gloomy, should remain as chancellor.
Amid talk of supporters of a "soft Brexit" joining forces to put pressure on the government, ex-Tory education secretary Nicky Morgan said most MPs wanted "a sensible deal that protects our economy and supports jobs".
While the UK would be "resilient" whatever happened, she told ITV's Peston on Sunday that she was dismayed that some of her colleagues were talking up a no-deal Brexit as a "favourable outcome".