Some residents, who were also hit by the 2015 Boxing Day floods, said they could no longer afford insurance.
Storm Dennis will bring a disruptive spell of weather over the weekend, and there are warnings in place for strong winds and heavy rain.
"Wet and very windy on Saturday".
"Because the rain came though so strongly and the river rose so quickly, we physically wouldn't have had time to put the barriers up".
There is also an amber warning for rain on high land to the west of York on the Yorkshire Dales, which could then feed in to York's already high river levels.
The Met Office has issued multiple National Severe Weather Warnings for wind and rain from Saturday through to Monday, including several amber rain warnings for parts of England and Wales.
Last weekend, Storm Ciara brought gusts of more than 90mph in places.
The two yellow warnings for wind and one for rain start at 10am on Saturday and run all the way through midnight on Sunday.
"The strongest winds are likely to be on Saturday afternoon and evening, with a lull overnight, before increasing again during Sunday".
Higher locations could have rainfall levels of 50mm to 80mm over the course of the weekend, potentially rising to 140mm in some parts, Mr Box said.
More widely, rain totals could be around 20mm to 40mm, with the Environment Agency urging people to check for flood warnings.
Flood defences in York.
The Environment Agency said there is a "heightened risk of flooding" across much of southern, central and northern England this weekend.
This includes the Foss Barrier in York, the Thames Barrier in London and another in Bewdley, Worcestershire, on the River Severn.