Political leaders in northern England have urged the government not to return to “business as usual” after the coronavirus lockdown, but to embrace positive changes the measures have led to, such as the drop in UK air pollution.

Andy Burnham, the mayor of Greater Manchester, and Steve Rotheram, the mayor of Liverpool city region, said building cycling and walking networks in cities and boosting internet connections so that more people could work from home could form part of a strategy to “keep some of the benefits that we’ve been experiencing”.

They also suggested a national programme to retrofit homes across the country with renewable energy technology could help to reboot the economy and create thousands of jobs.

Speaking during a press conference on northern England’s financial recovery from the pandemic, Burnham said: “There needs to be a new normality where we improve things. We ask for the public’s patience because we’re going to build back better.

“I think people do want to keep the cleaner air, they do want to keep exercising, they do want maybe have a more flexible working life where they don’t have to go in the office every day.”

As part of the set of sweeping changes the mayors said could be delivered locally to build a “cleaner, safer, stronger and crucially fairer” society, they also urged the government to ensure that key workers – such as care workers and shop assistants – were paid fairer wages and given more job security.

“We need a national reevaluation of work – how it is rewarded. We need to, I think, reflect on the fact that people have been overvalued at the top and undervalued at the bottom,” added Burnham.

Quick guide Will there be a second wave of coronavirus? Show Hide In recent days the UK has seen a sudden sharp increase in Covid-19 infection numbers, leading to fears that a second wave of cases is beginning. Epidemics of infectious diseases behave in different ways but the 1918 influenza pandemic that killed more than 50 million people is regarded as a key example of a pandemic that occurred in multiple waves, with the latter more severe than the first. It has been replicated – albeit more mildly – in subsequent flu pandemics. Until now that had been what was expected from Covid-19.

How and why multiple-wave outbreaks occur, and how subsequent waves of infection can be prevented, has become a staple of epidemiological modelling studies and pandemic preparation, which have looked at everything from social behaviour and health policy to vaccination and the buildup of community immunity, also known as herd immunity. Is there evidence of coronavirus coming back in a second wave? This is being watched very carefully. Without a vaccine, and with no widespread immunity to the new disease, one alarm is being sounded by the experience of Singapore, which has seen a sudden resurgence in infections despite being lauded for its early handling of the outbreak. Although Singapore instituted a strong contact tracing system for its general population, the disease re-emerged in cramped dormitory accommodation used by thousands of foreign workers with inadequate hygiene facilities and shared canteens. Singapore’s experience, although very specific, has demonstrated the ability of the disease to come back strongly in places where people are in close proximity and its ability to exploit any weakness in public health regimes set up to counter it. In June 2020, Beijing suffered from a new cluster of coronavirus cases which caused authorities to re-implement restrictions that China had previously been able to lift. In the UK, the city of Leicester was unable to come out of lockdown because of the development of a new spike of coronavirus cases. Clusters also emerged in Melbourne, requiring a re-imposition of lockdown conditions. What are experts worried about? Conventional wisdom among scientists suggests second waves of resistant infections occur after the capacity for treatment and isolation becomes exhausted. In this case the concern is that the social and political consensus supporting lockdowns is being overtaken by public frustration and the urgent need to reopen economies. However Linda Bauld, professor of public health at the University of Edinburgh, says “‘Second wave’ isn’t a term that we would use at the current time, as the virus hasn’t gone away, it’s in our population, it has spread to 188 countries so far, and what we are seeing now is essentially localised spikes or a localised return of a large number of cases.” The overall threat declines when susceptibility of the population to the disease falls below a certain threshold or when widespread vaccination becomes available. In general terms the ratio of susceptible and immune individuals in a population at the end of one wave determines the potential magnitude of a subsequent wave. The worry is that with a vaccine still many months away, and the real rate of infection only being guessed at, populations worldwide remain highly vulnerable to both resurgence and subsequent waves. Peter Beaumont, Emma Graham-Harrison and Martin Belam

Rotheram said the measures would form part of a “new economic model”, which put communities “at its heart”.

He added: “I don’t want to return to what we had before, because it was broken and this is our opportunity to fix it.”

The Office for Budget Responsibility last week said Britain’s economy could shrink by 35% this spring and unemployment soar by more than 2 million as a result of to the coronavirus crisis.

However, despite the potential cost of their proposals, Rotheram emphasised it was important to begin planning for economic recovery, adding: “If we don’t plan for recovery, we’ll have no economy to call on.”

The mayors’ calls come as pressure continues to grow on ministers to provide greater clarity on the country’s lockdown exit strategy.

Measures to curb the spread of Covid-19 announced by Boris Johnson on 23 March will remain in place before a review in just over two weeks’ time, but little is known how and when they will be lifted.

Burnham also asked for a city region mayor to attend Cobra meetings alongside the London mayor, Sadiq Khan, and the first ministers of Scotland and Wales, in order to represent the regions.