There’s nothing quite like a royal wedding to get the British to part with their cash, so in one respect the idea that the new Duchess of Sussex could be good news for the economy is a statement of the blindingly obvious. Retailers have had a tough time recently, and a bit of Meghanmania was just what they needed to get the tills ringing.

Interest in the newest member of the royal family will linger longer than the feelgood factor. People are clearly fascinated by her backstory and take notice of what she thinks. Role models are important, and just as it matters that Christine Lagarde sees fighting for women’s rights as a vital part of her job as head of the International Monetary Fund, so it matters that the Duchess of Sussex calls herself a feminist and wants to champion female empowerment. Feminism is an economic issue.

Plenty of explanations have been canvassed for Britain’s recent woeful productivity record: too little investment, poor infrastructure, insufficient spending on research and development, too many low-paid, low-skilled jobs, weak management and a long tail of under–performing firms among them. Strangely, the one that gets the least attention is the failure to utilise fully the skills of the available workforce.

Women outperform men in higher and further education, yet their talents are being wasted. Women and men are not equal partners in the workplace and the gap between them remains large despite some progress in recent decades. A report by McKinsey in 2015 said that advancing women’s equality could add $12tn a year to the world economy – equivalent to the economies of Britain, Germany and Japan combined. As David Coates says in his new book, Flawed Capitalism, an enormous pool of human capital is being squandered because of sexist cultures, glass ceilings and economic structures that make it hard for women.

The evidence for this starts right at the top of British society. Five out of 21 permanent secretaries in Whitehall are women; there is one women out of nine members on the Bank of England committee that sets interest rates; there has never been a female chancellor or cabinet secretary. When Moya Greene steps down from the Post Office in the summer, there will be just six women running FTSE 100 companies.

The Labour governments from 1997 to 2010 sought to address gender issues in the economy in a number of ways: through the tax and benefits system, by introducing a national minimum wage, by providing financial help with childcare, and by making maternity pay more generous.

Many of those gains have been rolled back over the past eight years. Tax credits have been made less generous; Sure Start centres have been closed; and job cuts in the public sector have disproportionately affected women. Austerity has had a gender dimension. Meanwhile, the way in which workplaces are organised is unfit for purpose in an age in which brains are more important than brawn.

Childcare remains a big problem. The gender pay gap will never be closed while women take most of the responsibility for childcare, because they are out of the workplace in their 20s and 30s and lose out on promotion to men who are often less qualified to do the job.

Many parents make the choice to look after their young children, but incentives for women to get back to work quickly after having children are weak, because expensive childcare combined with low wages means that the sums simply don’t add up. The Organisation for Economic Cooperation and Development has said the cost of childcare as a share of wages is higher in the UK than in any other rich developed nation. As a consequence, many women take the decision to look after their young children rather than return to work.

There is an obvious solution to this problem – a nationwide system of universal free childcare that would start from when a child is six months old. On the face of it, this would be an expensive commitment, although the Women’s Budget Group says it would pay for itself.

Upfront costs are certainly high – £33bn a year if the staff hired to run the scheme were paid at current wage rates, and £55bn a year if they were paid the same salaries as primary school teachers.

But this assumes that all parents would take up the offer immediately, which they almost certainly wouldn’t. A more realistic cost, as suggested by the Women’s Equality party, would be £28bn a year, which would be offset by the additional revenue the exchequer could expect to get. More women would be working, so income tax and national insurance receipts would go up. The new entrants to the workforce would have more money to spend and so extra VAT would be paid. Finally, the bill for benefits would go down. In all, the Women’s budget group says this adds up to just under £27bn a year.

If the government plumped for the more expensive £55bn a year option, the Women’s equality party says, it could raise £28bn by introducing a single rate of pension tax relief at about 25%, postponing further cuts to corporation tax, unfreezing fuel and alcohol duties, and reallocating the money it already spends on childcare and early education.

The wider economy would also benefit because better-educated and better-qualified women could be expected to make smarter decisions than men, if only they were in a position to make them.

Recent trends are perfectly illustrated by the Harry and Meghan match. He struggled at school and went off to join the army rather than go to university; she got a double major in theatre and international relations and has had a successful acting career. If the monarchy were abolished and the members of the royal family had to fend for themselves, there’s little doubt which of the couple would be the more reliable breadwinner.

• Larry Elliott is the Guardian’s economics editor

• This article was amended on 24 May to include references to the Women’s Equality party