They want the chance to decide on the Governments final deal before Brexit.
The Labour Party have said they will keep all options open on Brexit, including a peoples vote.
Shadow Brexit Secretary Sir Keir Starmer also said no one was ruling out remaining in the EU, during the Partys conference in Liverpool.
Locally Chesterfield MP Toby Perkins has backed calls for a Peoples Vote on the governments final deal before we leave the EU;
"It's important the Government have an opportunity to put a proposal infront of Parliament.
"But if it''s rejected, or it's clear promises made in the run up to the referendum aren't gong to be delivered, the case for letting the people decide if this is what they were promised, becomes increasingly powerful".
Meanwhile local woman Lindsay Neal, who campaigns for the Peoples Vote, has explained why she feels the Public should have the final say on the deal, calling the second vote 'logical'.
"If you were buying a house, you put in an offer, get it surveyed. if it comes back with a dodgy roof you make a decision.
"What the peoples vote is trying to make clear to people is it's informed consent".
34,478 people voted to leave the EU in Chesterfield, totalling 60% of the votes in June 2016s referendum. Nationally 52% voted to leave.
The petition for the Peoples Vote currently stands at over 308,000 signatures.