Commenting on the bill, Ms Cooper claimed the country was "in a really risky situation with a serious and growing risk of no deal in 10 days' time".
Barnier said Britain could still accept the stalled deal negotiated by May, reiterating it was "the only way" for Britain to leave the bloc in an orderly way.
Most politicians, economists and business groups think leaving the world's largest trading bloc without an agreement would be damaging for the European Union and disastrous for the U.K. It would lead to tariffs imposed on trade between Britain and the European Union, customs checks that could cause gridlock at ports and which could spark shortages of essential goods.
European Union leaders have called a special summit on April 10 to consider any request from Britain for a delay to Brexit - or to make last-minute preparations for Britain's departure without a deal two days later.
The prime minister did not say if she had the agreement of her ministers for her plan. "To be clear, during any long extension there will be no renegotiation of the Brexit withdrawal agreement, no, never", he said.
Ford of Europe Chairman Steven Armstrong was speaking at a Ford event in the Netherlands Tuesday, the day after British lawmakers voted down a series of alternatives to Prime Minister Theresa May's Brexit deal with the EU. Pro-Brexit Brits, both in public and Parliament, believe too much independence has been given up to the European Union - particularly where it concerns border controls and immigration - and they want it back.
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The Cabinet is scheduled to meet for five hours Tuesday amid calls for compromise to prevent a potentially devastating no-deal exit.
"We are now in a really risky situation with a serious and growing risk of no deal in 10 days", she said.
May said that if she could not agree a unified approach with Corbyn, a veteran socialist who voted against joining the bloc in 1975, then the government would come up with a number of options on the future relationship with the EU.
Almost three years since the United Kingdom voted to leave the European Union in a shock referendum result, it is still unclear how, when or if it will ever indeed quit the European club it first joined in 1973.
The deadlock has already delayed Brexit for at least two weeks beyond the planned departure date to 2200 GMT on April 12.
Speaking on Tuesday before talks with Irish Taoiseach (prime minister) Leo Varadkar, Macron said the United Kingdom would only have itself to blame for a no-deal scenario.
Labour legislator Yvette Cooper, one of the bill's sponsors, says "we are now in a really risky situation with a serious and growing risk of no-deal in 10 days' time".
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A third proposal calling for any Brexit deal Britain strikes with the European Union to be put to a public referendum was defeated 292-280.
"The deal is a deal which can appeal both to people who voted leave and to people who voted remain", he told the BBC.
As UK lawmakers failed to settle on a majority option during the indicative votes process overnight, parliament will now debate on the next steps and a long extension tomorrow.
"It's up to London to say it, and to say it now", he said.
Juergen Maier urged lawmakers to keep Britain in a customs union with the EU, saying that would allow frictionless trade to continue.
A cross-party group of MPs will present a bill on Tuesday that would force the government to seek an extension to European Union membership to avoid a no-deal exit.
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