Her decision follows the group of former Conservative and Labour MPs’ failure to get a single MEP elected in the EU elections.
The Penistone and Stocksbridge Constituency Labour Party (CLP) has re-issued calls for her to resign to trigger a by-election.
The MP left the group along with fellow founder members Heidi Allen, Chuka Umunna, Gavin Shuke, Sarah Wollaston and Luciana Berger.
In a group statement, the MPs said they would be ‘returning to supporting each other as an independent grouping of MPs’.
“We are all immensely proud of the team of Change UK candidates and supporters who stepped forward to join us in making the unequivocal case for remain in the recent EU elections,” reads the statement, released on Tuesday.
“We believe that our priority right now must be to provide collegiate leadership to bring people together in the national interest.”
However, the step-down from the party has left members of the Penistone and Stocksbridge CLP confused and frustrated.
Pete Bevis, acting chairman of the Penistone and Stocksbridge CLP, had already called for Ms Smith to stand down in March when she defected from Labour.
Speaking to the Chronicle yesterday, he said: “We have the same views as before, whether she is part of a grouping or not.
“From the CLP’s point of view we standby what was said at the beginning. We think the democratic and proper thing to do is to stand down from her position. Let’s have a by-election and make it a democracy.
“I think they (Change UK) were people of various backgrounds and it didn’t seem that it was necessarily going to continue.
“The fact remains that she stood at the last general election with the support and finances and volunteering of Labour Party members. The right and proper thing to do would be to step down.
“Now she has left Change UK let’s see what her priorities are.”
The Chronicle tried to contact Angela Smith’s office but the MP is currently in recovery from a hip operation.
However, when she was asked about calls for a by-election in March, she said: “I am still the same person and my views have not changed.”