I left the job I loved at John Lewis to run to be the Conservative mayor for the West Midlands because I believed I could help restore pride in the region. That meant expanding the economy, and two years later, business growth is strong. However, alongside the cranes and new offices, rough sleepers are to be found in doorways and at mobile soup kitchens. Behind closed doors, there are thousands of people sleeping on sofas at the homes of friends or family, families in B&Bs and vulnerable people living in some of the worst-quality shared housing.

No one can take pride in that. We have made some progress in tackling homelessness, securing around £10m from the government to roll out Housing First, a model of homeless support developed in Helsinki, Finland. Some 73 homeless people have been given accommodation and support through the scheme since it was launched in the autumn. It’s a good start, but we need to go much further.

To tackle the wider issue, we need to “design out” homelessness from society, for example, through businesses willing to hire homeless people and offering employee hardship funds for when their workers go through tough times, and banks making accounts open to homeless people. It also means building thousands of high-quality, truly affordable homes and tackling the rogue landlords taking advantage of vulnerable people.

But the government also has to act to tackle welfare-related poverty. Local housing allowance is the element of universal credit paid to those who need it to rent a safe place to live. If you are looking for a one-bedroom self-contained flat in Birmingham, you are eligible for just £441.31 a month. This is the same as in 2016, yet private rents in comparable one-bedroom flats in Birmingham have gone up by 11% over the last three years. People under 35 are only eligible for £248.47 a month because they are expected to live in a bedroom with a shared bathroom, lavatory and kitchen, even if they’re unable to find suitable shared accommodation. No wonder that many people fall behind on their payments and end up being evicted.

Losing a private tenancy as a result of getting into arrears is the most common reason for becoming homeless. The government’s freezing of the local housing allowance rate has undoubtedly contributed to an increase in homelessness in the West Midlands.

Facebook Twitter Pinterest Tents in Milton Keynes: ‘Losing a private tenancy is the most common reason to become homeless.’ Photograph: Graeme Robertson/The Guardian

And these low local housing allowance rates have led many landlords to skimp on the upkeep of properties, leaving tenants in poor-quality housing, or to move into the supported housing sector to reap the higher rates of housing benefit available, often without providing the high-quality support services that are also needed.

There is an urgent need for the government to act, and it cannot wait until Brexit is sorted out. The new prime minister needs to increase local housing allowance to a level where 30% of rented homes in any area are affordable to everyone. We should make sure that the lower rate for shared accommodation only applies to those actually living in shared accommodation, regardless of their age. We should also crack down on poor-quality housing and consider introducing a higher rate of local housing allowance for good landlords who treat their tenants well. The government should also allow people to opt for the allowance to be paid directly to landlords.

We have a moral duty to tackle homelessness and these changes would make an immediate and significant difference. But there is also a return to the Treasury from increasing the local housing allowance: there will be less need for costly temporary accommodation and fewer people getting into a spiral of health issues that burden the NHS and public services.

I will continue to challenge the government on the urgent need to address homelessness. On this issue I am joining Crisis and other homelessness charities to campaign for these changes. We previously called for the government to scrap its policy of stopping young people under the age of 21 from automatically getting housing benefit, and it listened. I hope that the new prime minister will listen on this issue.

• Andy Street is mayor of the West Midlands