“It was never my intention to nibble around the edges with policies of timid maintenance; I ran to take dead aim at the crisis of our time” said New York Mayor Bill de Blasio speaking about his attempts to tackle his city’s inequality, at Labour’s conference last month.

He explained how his Mayoral campaign began, with a few hundred people gathered outside his house; he was dismissed as naive and populist. But New Yorkers recognised his ‘Tale of Two Cities’ – of a ballooning gap between the richest and the rest – and ignored the establishment lament that speaking of inequality is “unconstructive, divisive… [and] harmful.” He swept to a convincing victory.

London is not too dissimilar. We are regularly told we live in the ‘greatest city in the world’ (main rival: New York), home to some of the world’s biggest businesses and richest people, its most highly-rated restaurants and art and music and sport, and we regularly takes top spot in rankings of the ‘world’s best cities’.

But a closer look reveals we tend to score well on all the things that don’t much matter to most citizens – ‘technology readiness’, ‘economic clout’, business-friendly tax rates or the convenience of the time-zone for financial trading – and perform very badly on those indicators that actually affect the quality of life of most Londoners – the cost of living, housing and transport, access to green space, health, safety, or a sense of community. The same day as de Blasio was speaking, another survey declared London the world’s most expensive city.

A third of our children grow up in poverty. The poorest Londoners can die up to 25 years earlier than the richest. Our highest-paid executives earnt more by January 8th than the average Briton will earn all year. The average house price increased by twice the average wage in 2013.

The greatest city in the world, perhaps, but for whom? And at what?

Our third London Paper – launched late last month – draws on ideas shared on Changing London over last winter to argue that we need a new definition of success for our city. The ever-growing inequality between the richest and the poorest – increasingly between the richest and the rest – is not simply an unfortunate by-product of progress but its antithesis. The public agree – three quarters of Londoners would support government action to close the gap between low and high earners.

We suggest four principles to underpin a new vision for London:

On poverty: Having enough to live on should be an entitlement in a rich city, not a privilege

The Mayor should push for a living wage in the lowest-paying sectors and properly enforced London and sector specific minimum wages, stronger trade unions, more support to improve skills and lower living costs, and routes into decent jobs particularly for our young people.

On wealth: Remuneration distorted beyond the dreams of avarice is no more useful here and no more welcome than abject poverty.

The Mayor should campaign for company pay ratios and greater transparency on executive pay, workplace democracy and higher taxes on wealth.

On business: Businesses of good character are defined not by shareholder return or contribution to GDP, but by the difference they makes to the lives of Londoners.

We need a Mayor’s Pledge, which employers are harried to sign, setting out our expectations of a good London employer:

• To pay at least the Living Wage so every London worker has enough to live on
• To pay highest-paid staff no more than 75 times the median, to publish the company pay ratio, and to introduce an employee onto the board to constrain excessive pay
• To willingly pay the taxes government expects to receive
• To ensure fair opportunities for young Londoners by offering apprenticeships and paid internships.

The Mayor should show their support for London’s biggest business by buying a share in each and asking them to commit to the Pledge at their AGM.

On housing: Houses in London are for people to live in and there must be enough for everyone. They should no longer be mistaken for investment vehicles.

We need a London Housing Challenge, with senior representatives from across the sectors led by the Mayor, to agree the most ambitious housing plan for London since the 60s, and set about building it.

In the Centre for London’s recent detailed and evocative exposition on the plight of London’s not-quite-lowest-paid, the authors say: “London cannot judge its success solely by the evanescence of trendy hipsters and tech entrepreneurs in Hackney and Shoreditch, the money flowing through banks in the City and Canary Wharf, and the wealth in Kensington and Notting Hill. London needs to bridge the gap between all it has to offer and those to whom it is currently failing to deliver this potential.”

This is not quick-fix politics: it calls for sustained stewardship of our city and its economy. But a bold mayor could lead that conversation, challenge the orthodoxy and ultimately change not just London but the national trajectory too