In a letter to Boris Johnson, the Labour Party leader called for the government to ensure “every resource is being utilised to aid those that need it and protect against future potential floods”.
He also said that the Mr Johnson should make sure the insurance industry "fulfils its responsibilities" and recompense victims who have incurred damage.
“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," Mr Corbyn wrote, as he called for a gathering of the COBRA emergency committee.
Residents of a community in flood-hit South Yorkshire have said they are worried the flooding could get worse as more rain is forecast later this week.
Severe flood warnings remain in place on the River Don, which burst its banks last week, leaving houses inundated by floodwater and residents forced to leave their homes.
Those living in Fishlake, near Doncaster, also raised concerns that more flooding was likely unless the existing water was pumped away.
The Met Office warned that frequent, heavy showers in these areas are “likely to cause some flooding and transport disruption” and that “flooding of a few homes and businesses is likely”.
Stephen Gilleard, a farmer in Fishlake, where around 350 residents left their homes after floodwaters rose last week, said he had never seen flooding like this.
He said: “There’s a pump on the main drain, that’s not going, drains haven’t been cleaned, the river needs dredging, every combination has just made the job worse, that’s my opinion.
“You learn to live with nature and, as a farmer, you deal with things but you can’t deal with this.
“There’s a lot of volume of water here to move, we’ve still not got no pumps in place starting to get rid of any of it, it’s a bad forecast for Thursday, more rain to come, and, unless we move some of this water, there’s no room for any more.”
Pam Webb, the owner of Truffle Lodge, a luxury spa in Fishlake, said the community had not experienced flooding in 100 years and said residents needed to know why it had happened now.
She said: “We need to now establish why and how and who should be accountable.
“Is it the flood defences that weren’t sufficient to hold it? Did something give at some other point?”
She added: “I’m not taking anything away from Sheffield, that’s great, work was done there but has it exacerbated the problem down here and we’ve now got a bigger problem here because of what happened there?”
Ms Webb said the Environment Agency was bringing in pumps after she made a direct appeal and it was now assessing where to put the equipment to begin pumping out the floodwater.
In the Bentley area, a military helicopter worked through the night to bolster flood defences.
Water levels in Fishlake appeared to be getting lower on Monday but the Environment Agency warned it expected river levels to rise again across the River Don catchment, with rain forecast in the area on Thursday night.
Downpours last week meant several areas from Yorkshire to Derbyshire and the East Midlands were deluged with one month’s worth of rain in a day.
One woman died after being swept up in floodwaters.
The body of Annie Hall, the former High Sheriff of Derbyshire, was found in the River Derwent on Friday morning after she was engulfed by floodwater in Darley Dale near Matlock.
On Sunday, Mr Johnson said he was “in awe” of flood-hit communities’ “spirit and resilience” after he visited Matlock.
Doncaster Council praised the “fantastic community effort” of those donating food to Custom Windows and Doors shops in Bentley but said they did not need any more.
A spokesman said the team “can no longer facilitate the donations, with food going to waste” but added: “Cleaning products would be greatly received.”
A JustGiving page for those affected by flooding has raised more than £49,000 since being set up two days ago by South Yorkshire’s Community Foundation.