In a letter sent to flooding minister Rebecca Pow, Mr Jarvis said the November floods had a devastating impact across many parts of South Yorkshire, with almost 1,000 homes and 560 businesses affected and many still facing repair work or unable to return home.
And he said coronavirus has added to the problems facing communities already hit hard by the floods.
The Government previously announced it would double its investment into flood prevention to £5.2bn over the next six years.
And Mr Jarvis said: “Accelerating the delivery of this funding would provide vital protection to many homes, families and businesses, help us adapt to our changing climate and act as a crucial economic stimulus in response to the Covid-19 pandemic.”
He added: “It is urgent that we do everything we can to stop devastating floods hitting again. We cannot let the people of South Yorkshire down.”
Mr Jarvis reminded the Government of the commitment to hold a Flooding Summit to bring together local authorities, Government, and agencies to create a plan for flood defences in South Yorkshire and across the North of England, including South Yorkshire’s Don river valley.
“The Government is rightly focusing much of its energy on the Covid-19 crisis, but the Government has to follow through on their commitments,” he said.
“It is now seven months since the Prime Minister promised to hold a flooding summit so we can take more coordinated and effective action. The clock is ticking.”
He also called for the funding promised by the Government to invest in flood defences to be spent in close collaboration with devolved authorities like the Sheffield City Region, which had developed a detailed programme for prevention and resilience works based on local knowledge and consultation.
The programme would protect 2,826 businesses and 10,365 residential properties from flooding – representing a positive economic impact of more than £1.7bn in direct damages avoided alone.
Mr Jarvis said: “It’s not just about the amount of money, it’s how it is spent. We need to do this in a way which reflects local priorities and concerns and helps our local economy and environment.
“Approaches like Natural Flood Management and a major tree-planting programme will not only reduce our flood risks but create jobs, improve the quality of life in our neighbourhoods, reduce our carbon impact, and create new natural habitats.”
He added: “Intelligent flood prevention work is exactly the sort of spending we should be doing in response to this [coronavirus] crisis.
“We have to make sure the major public spending that is so obviously needed to help keep the economy afloat actually produces some long-term good. We can aim so much higher than just returning to the status quo.
“Now is exactly the time to put people to work on transforming our region and our economy. We have to build back better – and what better way than ensuring we never see the devastation caused by these floods again.”
A Defra spokesperson said: “We understand the heartbreak, devastation and disruption faced by communities when flooding hits and we are committed to making the country as resilient to flooding as possible.
“This is why we have already built 59 new flood defences in Yorkshire since 2015, better protecting 13,200 homes, and nationally we have doubled our investment to £5.2bn over the next six years to better protect 336,000 properties.
“We will continue to work with local leaders and communities across Yorkshire to reduce the risks of flooding to as many people as possible.”