Sadiq Khan will be settling into his new office at the top of City Hall. Here are the five areas that should be at the top of his to-do list.

The jubilation that followed a hard-won and decisive victory will soon dissipate as the scale of the task facing him fast becomes very real. The energetic new mayor will be bombarded with calls for action across the full range of his responsibilities.

The first priority for the new mayor must be tackling the capital’s housing crisis. The London Housing Commission set out a practical programme for the new mayor to follow, much of which was welcomed and adopted by the candidates prior to the election. But to truly put this radical plan into action the mayor’s team will need to quickly identify and make available more land, work with housing associations and house builders to ratchet up construction rates of affordable homes, and ensure the planning system has a bias towards new development.

All politicians promise more homes but few deliver them, and with 50,000 new homes a year promised, the new mayor must be the exception. Khan will need to be bold and determined if he is to buck the trend of over-promising and under-delivering. He should use his commitment to build as a point of negotiation with the treasury on releasing additional powers to allow the capital to tackle the crisis in its own way, such as allowing the mayor to name and shame boroughs and other public bodies that are failing to identify enough land for homes. The NHS in London, for example, owns land three times the size of Hyde Park, with much of it underused. Londoners are not well served by the failure to build on this public land. Finally, Kahn could review and expedite private and greenbelt land near public transports sites for housing development, in exchange for improved community amenities and greenbelt protections in other places.

One memorable promise from the campaign has been Khan’s commitment to freeze transport fares in the capital. In addition, he has promised a one-hour bus ticket, no changes to concessionary fares, and retaining the costly Oyster card system. The enormous costs are supposed to be financed by back office savings and a new trading arm that seem optimistic at best and wildly unrealistic at worst. A more realistic method of raising the required revenue would be an expansion in road-pricing beyond the congestion charging zone.

Road pricing has the added attraction of improving the environment and helping to address London’s alarming air pollution problem, which is responsible for close to 10,000 early deaths and costs the city around £3.7bn a year. Establishing a ‘Clean Air Zone’ in the capital would be a major step forward, and is supported by business group London First as well as environmental campaigners such as Greenpeace, and backed by IPPR. It would be a bold move that would build on Khan’s impressive coalition-building skills so evident in his campaign.

Across the pond, former New York City mayor Michael Bloomberg made promoting health the signature achievement of his time in office. Ara Darzi’s ambitious report Better Health for London was jam-packed with fresh thinking on how to improve the health of the capital. With Boris Johnson’s attention focused on Downing Street rather than City Hall, little of this agenda was taken forward. From tackling air pollution and childhood obesity to making parks and public spaces smoke free, improving health has the potential to animate Khan’s mayoralty.

Finally, building on his existing responsibility for the Metropolitan Police, the mayor should push central government to devolve responsibility for the wider criminal justice system to City Hall. Khan’s commitments to reduce crime and improve the safety of the capital’s streets would be greatly enhanced if he were able to take a holistic approach. As IPPR points out, with control of prevention, prisons and probation services, the mayor would be equipped to make meaningful improvements to justice and improve the lives of all Londoners.

Socialism – or even social democracy – is all about priorities. Housing. Transport. Environment. Health. Justice. It is a long list but it should not be a surprise that the mayoral inbox is piled high. After all, during his time as mayor, Boris Johnson found time to write two books, contest and win a parliamentary seat, lead the campaign to leave the European Union, and pursue his own bid for No.10. Now Londoners have a full time mayor again, they will rightly expect that he gets quickly to work on their behalf.

This article was published first on the Times Red Box, and is republished here with their permission.