.Mr Corbyn, on a visit to businesses in the city devastated by the 2015 floods, said the Government should “cough up” as they had pledged to do.
The Boxing Day floods brought by Storm Eva in 2015 damaged more than 700 businesses and nearly 3,000 homes, mainly in the Kirkstall area of the city, on the banks of the River Aire.
The Climbing Lab on Kirkstall Industrial Park off Kirkstall Road was just about to open when it was flooded, causing £30,00 damage to stock and materials.
Mr Corbyn visited the Climbing Lab soon after the flood and fulfilled his promise to revisit the business today (Thurs Oct 4).
He scaled a climbing wall after discussing challenges faced by businesses next to the River Aire with Hannah Mason, one of the Climbing Lab’s three owners.
Hannah Mason said: “I have no doubt that we will flood again.
“I’m creating a business that I want to be successful, but at the same time there is this threat that could wipe it all out.”
Labour claim the Government has broken promises to fund flood defences to protect against a once in 200 year flood - instead opting for a cheaper option of defences protecting against a once in 75 year flood.
A cross-party delegation of eight local MPs and council leaders have a meeting with Floods Minister Theresa Coffey later this month to ask for the £47 million they say is lacking to protect the city from future flooding.
Mr Corbyn said: “I was in this very place in December 2015, when it was being flooded and the volunteers were amazing, the community support was fantastic.
“Unless the Government now funds the next stage of flood protection for Leeds then there are going to be problems ahead.
“In January 2016 I asked David Cameron in Prime Minister’s Question Time for a guarantee for the flood protection scheme in Leeds.
“He promised it would be funded, he said there would be no problem with central government money for flood protection.
“Here we are now nearly three years on, and it still hasn’t happened."
Leeds MPs Rachel Reeves and Hilary Benn accompanied Mr Corbyn on the visit to businesses hit by the floods and will head the delegation to Government on October 17.
Mr Benn said one German-owned engineering firm had left the city after being flooded, with the loss of 95 skilled and well-paid jobs.
Ms Reeves said businesses who stayed were worried of more floods and were struggling with insurance costs which had increased five fold while the Government now offered “second rate” flood prevention.
She said: “It’s a series of broken promises. Rory Stewart, Liz Truss, they are not giving what’s promised. We are £47 million short of what’s needed.”
A Department for Environment, Food and Rural Affairs (Defra) spokesperson, said: “We remain committed to better protect Leeds from flooding. We have already spent £33 million and have committed a further £35m between now and 2021 to better protect properties and businesses in Leeds.
“The outline business case submitted by Leeds City Council to the Environment Agency in July did not fully justify the request for further government funding as it did not offer value for money to the taxpayer.
“The Environment Agency are expecting to receive an updated case within the next week.”
Labour leader Jeremy Corbyn gave a strong and stable performance that revealed his Action Man tendencies as he scaled a wall at the climbing centre.
While Mr Corbyn had been told by his wife ahead of the visit “no dancing”, following the Prime Minister’s shimmy before her conference speech on Wednesday, she had made no mention of the 69-year-old not climbing.
“Please don’t tell my wife,” he said to an aide.
After chatting to staff, Mr Corbyn, who keeps fit by working on his allotment, whipped off his linen jacket and scaled a climbing wall to cheers and shouts of “Go on Jeremy!” from other climbers.
Gripping the hand holds and resting his feet on the supports as he went, Mr Corbyn climbed halfway up a 30-foot wall.
He shouted down with a smile to the gathering of cameras and reporters below: “Hello folks, how you doing? The future’s good with Labour - even higher with Labour.”
Mr Corbyn added: “If I fall down will you all turn the cameras off? Is that a deal?”
Ms Mason, one of the Climbing Lab’s owners, said after Mr Corbyn’s climb: “He is very good at climbing. He has got a natural talent for it.”