In a letter to the Prime Minister Mr Corbyn urged Mr Johnson to “take personal charge of the government’s response to the devastating flooding we have seen over the past few days”.
He said: “We need full assurance from the Government that every resource is being utilised to aid those that need it and protect against future potential floods”.
It comes after the Prime Minister's visit to Matlock in Derbyshire on Friday, in which he said flooding "is not looking like something we need to escalate to the level of a national emergency".
But Mr Corbyn said: “With dozens of flood warnings still in place, I have to disagree with your assessment from the weekend that this is not a ‘national emergency’. If this had happened in Surrey, not Yorkshire or the East Midlands, it seems far more likely that a national emergency would have been declared.
“Every year we don’t act means higher flood waters, more homes ruined and more lives at risk due to climate change.”
He added: “I urge you again to hold a COBRA meeting to ensure all is being done to help the families affected.”
Derbyshire High Sheriff Annie Hall died on Friday after being swept away by flood water.
Mr Johnson said the government had set aside billions for flood defences and preparations due to an increase in serious flooding “perhaps because of building, almost certainly because of climate change”.
He said: “You’ve got to face the reality that places like this are vulnerable to flooding – we’re going to see more of it.”
The Met Office today had a yellow weather warning for rain in place until midday tomorrow, covering parts of Stoke-on-Trent, Derby and Sheffield.