MPs will vote within hours on whether to ask the EU for permission to delay Brexit beyond the 29 March departure date.
It comes after MPs voted on Wednesday evening (UK time) to reject a no-deal Brexit under any circumstances.
Prime Minister Theresa May could also make a third attempt to get her EU withdrawal deal through Parliament in the next few days.
The EU said there were two ways the UK could leave - with or without a deal, adding it was ready for either outcome.
The British government said there could be a short delay to Brexit - or a much longer one - depending on whether MPs backed the prime minister's existing withdrawal deal, which has been agreed with the EU, by 20 March.
If MPs approve Mrs May's deal before next week's EU summit in Brussels, then the extension will be until 30 June.
However, the PM warned that if the deal - which has twice been rejected by overwhelming majorities - is not approved, a longer extension will be needed, requiring the UK to take part in elections for the European Parliament in May.
"I do not think that would be the right outcome," said Mrs May. "But the House needs to face up to the consequences of the decisions it has taken."
In a night of high drama, the Commons first voted on an amendment to reject Britain exiting the EU without a deal by a margin of four.
Then, in another vote, they reinforced that decision by 321 to 278, a majority of 43.
That vote was on a motion that originally said the UK should not leave the EU without a deal, specifically on 29 March, but with the option of a no-deal Brexit at any other time.
It had been the government's motion.
The government had wanted to keep control of the Brexit process, and keep no-deal on the table, so they ordered Conservative MPs to vote against their own motion.
That tactic failed. Government ministers defied those orders and there were claims Mrs May had lost control of her party.
Thirteen government ministers - including Work and Pensions Secretary Amber Rudd, Business Secretary Greg Clark, Justice Secretary David Gauke and Scottish Secretary David Mundell - defied the government whips by abstaining in the vote.
Work and pensions minister Sarah Newton voted against the orders of the whips and has now resigned.
Mr Mundell said he backed the prime minister's deal and had always made clear his opposition to a no-deal Brexit.
However, the no-deal vote is not binding. Under current law the UK could still leave without a deal on 29 March, unless an extension is agreed with the EU.
Speaking after the result of the vote was read out, Mrs May said: "The options before us are the same as they always have been.
"The legal default in EU and UK law is that the UK will leave without a deal unless something else is agreed. The onus is now on every one of us in this House to find out what that is."
MPs also voted by 374 to 164 to reject a plan to delay the UK's departure from the EU until 22 May 2019, so that there can be what its supporters call a "managed no-deal" Brexit.
This amendment was known as the Malthouse Compromise - after Kit Malthouse, the government minister who devised it.
Corbyn seeks a compromise solution
Labour leader Jeremy Corbyn said that Parliament must now take control of the Brexit process and his party will work across the House of Commons to seek a compromise solution.
The DUP - which twice rejected Mrs May's deal in the Commons - said it was due to have talks with the government on Thursday to see if a solution could be found allowing its MPs to support Mrs May in a future vote.
A party spokesperson said they wanted to find "a sensible deal for the entire UK and one that works for our neighbours in the Republic of Ireland".
BBC Europe correspondent Kevin Connolly said that before approving any extension to Article 50 - the legal instrument by which the UK will leave the EU - EU leaders would want to know "how long an extension the UK requires and how it proposes to use the time".
A European Commission spokesperson said: "There are only two ways to leave the EU: with or without a deal. The EU is prepared for both.
"To take no deal off the table, it is not enough to vote against no deal - you have to agree to a deal.
"We have agreed a deal with the prime minister and the EU is ready to sign it."