Over 13,000 people in Milton Keynes have signed a petition calling for the United Kingdom to revoke 'Article 50', the legal mechanism for the country to leave the European Union.
It comes as over three and a half million people nationally have signed the petition on the official government website.
There are 6,790 signatures claiming to be from people in Milton Keynes North and 6,405 from Milton Keynes South.
"The government repeatedly claims exiting the EU is 'the will of the people'," the petition says.
"We need to put a stop to this claim by proving the strength of public support now, for remaining in the EU. A People's Vote may not happen - so vote now."
The petition has had the highest rate of signatures on record - and at one point, it caused the official petitions website to crash.
But it does not appear to have swayed Mrs May, who said after meeting EU leaders about a delay to Brexit: "I do not believe that we should be revoking Article 50."
There was a surge in support following the prime minister's Downing Street speech on Wednesday.
She has repeatedly refused to reverse Brexit - pledging to deliver on the result of the 2016 referendum that saw more than 17 million people, 52% of those who voted, back the UK's departure from the EU.
In Wednesday's speech, Theresa May pinned the blame on MPs for her move to seek a delay to Brexit from the end of this month to 30 June, telling voters: "I am on your side."
The PM was not granted her preferred extension date, instead being given a two-tier extension by EU leaders.
They softened the immediate threat of a no-deal divorce by offering a delay until 22 May if MPs pass Mrs May's deal by the end of next week.
But if parliament rejects it again in "meaningful vote three", the UK faces a new hard deadline on 12 April.
"Revoke Article 50" began trending on Twitter soon after the PM's speech on Wednesday night.
Actors Hugh Grant and Jennifer Saunders promoted the petition on social media, as did physicist Brian Cox.
More than 600,000 had signed the petition by 9am on Thursday, at which time the website reported an error message.
By 12.30pm, more than 800,000 had signed the petition with the website restored.
Almost 2,000 signatures were being added every minute during Thursday lunchtime, causing the site to crash multiple times.
A House of Commons spokesman said: "We know that the petitions website has been experiencing problems due to the number of people using the site.
"This is a mixture of people signing petitions and refreshing the site to see changes to the number of signatures.
"The majority of people are now able to use the website and we and the Government Digital Service are working to fix any outstanding problems as soon as possible."
When asked about the technical problems, Commons leader Andrea Leadsom said: "Should it reach more than 17.4 million respondents then I'm sure there would be a very clear case for taking action."
Mrs May's spokeswoman dismissed the petition, telling a briefing of reporters on Thursday that the PM "will not countenance" cancelling Brexit.
The petition has become the second most popular petition on the parliament website.
A petition from 2016 calling for a second referendum should the winning vote and turnout not meet a certain threshold is top of the pile with nearly 4.2 million signatures to date.
After it broke the 2 million mark it surpassed what was previously the second most popular - a petition opposing the prospect of a state visit from US President Donald Trump - at 1.9 million signatures.
The most popular pro-Brexit petition has 375,000 signatures. It calls on the government to leave without a deal at the end of this month.
Parliament's petitions website requires those signing petitions to tick a box confirming they are a British citizen or UK resident and give a name, email address, country and postcode.
A total of 960,000 signatories claim to be from the UK, followed by France (8,300), Spain (4,600) and Germany (3,700).
Signatures do not count if people do not click a link in a confirmation email, but signatories do not need to provide any proof of their address or citizenship.
Additional reporting by Sky News.