The MP for Penistone and Stocksbridge is one of seven Labour MPs who have quit the party in a major blow for leader Jeremy Corbyn.
Angela Smith announced her resignation along with Luciana Berger, Chris Leslie, Gavin Shuker, Mike Gapes, Ann Coffey and Chuka Umunna at a press conference in London this morning.
It follows disquiet over how the Labour leadership has handled the party's position on Brexit and concerns over anti-Semitism.
In a stinging attack on the party's recent difficulties, Ms Smith said: "Labour is a party now characterised by intolerance and fuelled by hatred for anything other than a hard left political agenda; it fosters division rather than unity and despises all those who dare to disagree with its fundamentalist approach to political debate."
Ms Berger said: "This morning we have all now resigned from the Labour Party. This has been a very difficult, painful, but necessary decision.
"We represent different parts of the country, we are of different backgrounds, we were born of different generations, but we all share the same values.
"From today, we will all sit in Parliament as a new independent group ofMPs."