The petition was created in May by (ironicaly) a LEAVE supporter who thought the vote would go the other way.There has already been a petition in London purporting to have a million signature calling for a second vote. I'm a cynic and a skeptic so I don't believe they actually got 1 million signature in 24 hours. I think they started this petition long before the vote.
Point is, retrogasm, that some parties are already calling for another vote.
The signatures aren't legit: Hundreds of thousands of signatures (maybe even over a million?) were put there as a 4chan prank. They set up autovoter bots to add millions of signatures.