Improving social mobility is "far more complex" than deciding whether a school is selective, Justine Greening has said.
The former education secretary's comments come after her successor, Damian Hinds, said he wanted to see existing grammar schools expand.
Ms Greening was speaking to Tes as she prepared to launch a new social mobility pledge, which will commit companies to work with schools to provide coaching and mentoring for children from disadvantaged backgrounds.
Improving social mobility was a key reason given by the prime minister, Theresa May, for her now-aborted plans to create new selective schools.
However, when asked about the role of grammar schools in improving social mobility, Ms Greening said: “I think perhaps the most powerful thing the government can do is to get on with putting in place the social mobility strategy that I launched immediately before Christmas, which contains a range of steps that need to be taken by the [Department for Education] to make sure the schools' standards rise across the country, but especially in the parts of the country that have lagged behind.
“I think what that strategy demonstrated was that tackling educational inequality is far more complex than whether a school is a grammar school or not."
When it was pointed out that her 43-page document, Unlocking Talent, Fulfilling Potential, did not mention grammar schools once, she laughed and said “no”.
Helping pupils from disadvantaged backgrounds
Ms Greening, who was sacked as education secretary in January, said the Confederation of British Industry, British Chambers of Commerce and the Federation of Small Businesses are supporting the pledge, along with 20 major companies, including BT, Adidas and ITV.
The first pledge reads: “I/we will partner with schools or colleges to provide coaching through quality careers advice, enrichment experience and/or mentoring to people from disadvantaged backgrounds or circumstances.”
Ms Greening told Tes that the pledge would not add to workload in schools “because it helps them”.
She added: “When children get the chance to see what the world of work is all about and the careers they can be aiming for, everything becomes much more real for them and they start getting really motivated about opportunity.
“That’s when they go back into the classroom and really understand why learning and paying attention and concentrating is so important.”
The other pledges commit companies to providing structured work experience or apprenticeship opportunities for people from disadvantaged backgrounds, and to adopting open recruitment practices to provide a level playing field for applicants.
Theresa May made improving social mobility a key pledge when she became prime minister, but last week the Commons Education Select Committee said the government needed to devote "far greater energy and focus" to the issue.
Asked why it had been left to her as a backbench MP, rather than the government, to create the pledge, Ms Greening said: “In a funny way, sometimes for government it almost needs someone independent to do this kind of campaign, and clearly now I’m not in government and am independent of government, so I can hopefully play a role doing what I’ve always said I want to do, which is building a coalition of the willing.”
She added: “I feel every single government department needs to be asking itself a very simple question, which is, what is the role it can play in backing up the DfE’s social mobility strategy to deliver an equal opportunity Britain?”
Asked whether government departments are doing this, she said: “I felt that 2018 was very much about the DfE now engaging across government to get other departments to weigh in behind the social mobility strategy that had been launched in December. I hope that work happens.”
Ms Greening added that she will be launching a new website to host the pledge, to coincide with a debate that takes place in Westminster Hall at 9.30am tomorrow.