The Rotherham-born MP and former Cabinet minister Justine Greening said she could be prepared to run for the Tory leadership if Theresa May resigns or is forced out.
The ex-education secretary - a former pupil of Oakwood High School in Rotherham - is campaigning for improved social mobility and called for a national effort to boost access to opportunities similar to that shown by the founders of the welfare state and NHS.
Although Ms Greening indicated she could run for the leadership if there was a vacancy, she insisted that she would prefer the Tory Party to change now in order to show what it can do to address the problem.
Ms Greening, a prominent pro-EU Conservative, quit Mrs May's Cabinet in January after refusing to be moved from the education brief.
She told ITV's Good Morning Britain; "Things need to change, don't they, and I think people need to have some hope for the future, that Britain can be a country that runs differently and more fairly than it does at the moment."
Asked if she would run if there was a vacancy, the Putney MP said: "I might be prepared to, but I'm more interested in the Conservative Party actually showing what it can do for this country."