A petition to Revoke Article 50 has now been signed by more than six million people.
Today EU Council President Donald Tusk said the six million people who have so far supported it must be listened to.
MPs will discuss the poll in Westminster Hall, a secondary chamber, on 1 April after a record number of people signed it.
But the government have already said they won’t be revoking Article 50.
In an official response posted on the parliamentary petitions website, the Government said: “This Government will not revoke Article 50. We will honour the result of the 2016 referendum and work with Parliament to deliver a deal that ensures we leave the European Union.”
Revoking Article 50 is one of eight options that MPs voted on.
Article 50 is the two-year legal countdown to Brexit that was meant to end this Friday, and is now set to end on April 12.
The Commons Petitions Committee said the petition is “the most signed petition ever received on the House of Commons and Government petitions site”.
The previous record was 4.1 million signatures on a petition demanding a second referendum on Brexit.
Britain needs EU leaders’ permission to extend it, but not to revoke it entirely.
Mr Tusk said today: “You cannot betray the six million people who signed the petition to revoke Article 50, the one million people who marched for a People’s Vote, or the increasing majority of people who want to remain in the European Union.
“I told some of you that if you compare Great Britain to a sphinx then the sphinx would seem to me an open book. We will see in the course of this week how this book will speak.”
Mrs May’s agreed to extend the UK’s membership until April 12 – or May 22 if she succeeds in passing her Withdrawal Agreement through Parliament.
On April 1 alongside the Revoke Article 50 poll, MPs will also debate petitions calling for a second EU referendum, which has received more than 120,000 signatures, and another – signed by more than 140,000 – demanding that the UK leave with or without a deal on March 29.
It comes after at hundreds of thousands of people marched on Parliament on Saturday to demand a second referendum on Brexit .
Organisers of the Put it to the People march claimed one million people joined the peaceful procession through the capital.
Parliament’s website crashed several times as it struggled under the weight of people signing the petition.
It has experienced the fastest ever signing-up rate of any petition and is by far the most popular of the current parliament.
It has also outstripped a petition backed by more than 1.8 million people calling for US President Donald Trump not to make a state visit to the UK.
More than 4million people signed another petition in 2016 which called for another EU referendum in the event that neither the remain or leave camps achieved 60 percent of the vote.