A petition on Parliament’s website calling for Brexit to be cancelled by revoking Article 50 has passed three million signatures.
The petition has attracted two million signatures in the past 24 hours.
Asked last night if it showed a rising anti-Brexit mood, Theresa May said the UK had already decided to leave in the biggest ever democratic exercise.
But Lib Dem MP Layla Moran said the petition could “give oxygen” to the campaign for another Brexit referendum.
“I hope the prime minister listens but she has a long history of not involving Parliament and not wanting to involve the people,” Ms Moran said.
European Council chief Donald Tusk has said revoking Article 50 is one of the options the UK has if MPs again reject Mrs May’s withdrawal deal.
The UK has to decide its next move by 12 April after the EU agreed a plan to delay Brexit beyond 29 March.
People signing petitions on the Parliament website are asked to tick a box saying they are a British citizen or UK resident and to confirm their name, email address, and postcode to sign.
Data from the petitions website suggested nearly 1.3 million of the first two million signatories were people living in the UK, with the remainder including 10,000 from France, nearly 6,000 from Spain and about 4,000 from Germany.
The breakdown of signatures by country of residence appears not to have fully updated since then.
In January, MPs debated whether the UK should leave the EU without a deal, after a petition calling for that got 371,673 signatures.
The prime minister plans to bring the agreement she has negotiated with the EU back to the Commons for the third time but MPs want other options to be considered as well.
Ms Moran said the deal on the table should be put to the public in a referendum, alongside the option to remain and if the public chose the latter, then Article 50 should be revoked.
“We have to find a way forward in the next week and I hope what this will do is give oxygen to the People’s Vote campaign,” she told the BBC.
“The People’s Vote remains an option because it is still compatible with Theresa May’s deal. If she wants her deal to stay alive, the People’s Vote is the way to do it.”
Speaking on Thursday night after the petition passed the two-million mark, Mrs May said the public had already had their say on EU membership.
“They voted in 2016, they voted to leave. I think the time is now to deliver for the British people, the time is now to make the decision.”
In December, the European Court of Justice ruled that the UK can unilaterally revoke Article 50 of the Treaty of the European Union.
This means the UK can decide to stay in the EU without the consent of the 27 other member states.
On Thursday, the petition calling for this quickly passed the 100,000-signature threshold needed for it to be debated in Parliament, garnering nearly 2,000 signatures a minute at one stage.
However, it is not the most popular ever on the Parliament website.
A petition for a second EU referendum in June 2016 attracted more than four million signatures and was debated in the Commons – but thousands of signatures were removed after it was discovered to have been hijacked by automated bots.