The Rotherham-born politician, who served as Education Secretary until last January, makes the case for a new approach to politics in her monthly column for The Yorkshire Post.
Her intervention comes at a time of constitutional crisis as the Government – and Houses of Parliament – battle for supremacy over the terms of Britain’s future relationship with the European Union.
MPs are likely to seek further powers next week after Theresa May’s EU Withdrawal Agreement suffered the biggest defeat in modern political history on Tuesday night.
But Ms Greening, a prominent Remainer and advocate for a second referendum, believes that public trust will only be won back if there is a change of approach after the Brexit process has reached its conclusion. “All of this comes on the back of a British electorate that has steadily grown more and more tired of some of the dysfunctional party politics that they see taking places,” she writes.
“A party politics that too often prioritises short-term, press-release politics playing to its core base, irrespective of whether that reflects the British public’s desire for working across parties if necessary, to take the long-term decisions that actually deliver for the British people and for future generations.
“Brexit is the latest, profound long term challenge Britain faces which people feel their political classes have failed to develop a strategy to deal with.
“Whether it’s social mobility, housing, social care or anything else, our party politics isn’t effective at resolving these big challenges. We spend too much time arguing between parties for the purpose of scoring political points and not enough time working cross-party to agree common ground.”