The latest warning comes as flood-hit locals in Cumbria are clearing up after the second deluge in three weeks.
Weather warnings are in place from the Met Office, prompting fears of further flooding in the North as the latest storm rolls in on Christmas Eve.
The Environment Agency said there was “the chance of seeing further flooding impacts for parts of the River Ouse in Yorkshire and the City of York over the coming days.”
Towns and villages in Cumbria, still dealing with the aftermath of Storm Desmond earlier this month, were flooded for the third time in a month on Tuesday, with Glenridding, Keswick and Kendal all hit again.
In Appleby, the River Eden burst its banks once more, causing localised flooding in the low lying Sands area of the town.
A flood warning siren prompted dozens of local people to rush to help - before the stone bridge over the river was closed as a precaution.
Martin Stephenson, a Cumbria County Councillor for Appleby, said from the riverbank: “We are not looking forward to the arrival of Eva, the next storm coming in on Christmas Day, having had two floods already.
“The first flood on the 5th of December was exceptional, it over-topped the defences.
“That was quite a blow.
“This second flood has been a normal flood. It is very prone to flooding, Appleby is noted for flooding, but normally just in the Sands area.
“Residents and businesses get used to the fact that flooding is a risk nearly all the time.
“Over the years they have built resilience to that.
“Even more resilience may need to be built into those areas looking forward.
“We had what was called a one-in-100-year flood two weeks ago. We seem to be getting far more of these severe floods. You then have to ask questions, do you need to do anything more?”
Sandbags and flood defence barriers stood in doorways while skips lined the main streets as council lorries cleared drains and gullies of debris damming water courses.
A low wall of around 3ft (1m) high, built in 1995 and equipped with hydraulic gates to seal off the centre of the town, has prevented flooding many times, but could not prevent the deluge earlier this month, Mr Stephenson said.
Patrick Leach, local resident and business owner of Capstick Carpets across from the river, was partially flooded on Tuesday, with the water lapping up to the inside step of his shop.
Mr Leach, who raised the floor level after the 2005 floods to make his premises flood-resilient, described the latest incident as a “normal flood” which was contained.
Earlier this month he lost up to £40,000 in stock and £30,000 in contents after 3ft (1m) of water flooded his shop and warehouse.
He said: “Except for a very extreme event, which happened two weeks ago, this floor should be higher than the water level.
“Yesterday we have our own flood defences for normal floods.
“You can protect against that flood but the one the other week, I don’t think anything can protect against that really.”
Mr Leach described the prospect of Storm Eva as “pretty concerning” but is preparing for the worst with his warehouse stock of carpet rolls moved up to roof height.
However, locals have been heartened by the response of neighbours living on higher ground to the sounding of the flood alarm for those in danger.
Mr Leach added: “They just turned up. We had somebody here helping us move things, putting flood gates up.
“If one person hears that siren he rings everybody else and says ‘Let’s go and help’.
“You might get maybe 100 people turn up. They fill sandbags. They just turn up and move things.
“Two weeks ago we filled 16 skips, most of those were filled by volunteers.
“Generally we can get through, it’s just trying to think one step ahead. We kept moving the gauge, if you like, so now we are moving it again. Just plan ahead.”
A multi-agency co-ordination group of police and local authorities in Cumbria was formally stood down as river levels receded and only two Environment Agency flood alerts, where flooding is expected, are still in place.
They are “monitoring the situation closely” but Storm Eva is set to batter Britain with more rain falling on already sodden fells and swollen rivers, and the worst weather for Cumbria expected on the evening of Christmas Day.
Paul Mustow, deputy director in flood and coastal risk management at the Environment Agency, said: “Our thoughts are with all those who have had their homes and businesses flooded throughout the run-up to Christmas.
“Staff are now on the ground taking action to support communities affected, as well as checking the condition of flood defences and the position of pumps and temporary flood barriers.
“The Environment Agency is also preparing for the possibility of further unsettled weather from Christmas Day into Boxing Day.
“More rain is forecast and this could lead to some disruption. In addition to Cumbria’s existing flood defences, the Environment Agency has transported over two kilometers of temporary flood barriers and more than 20 extra pumps to the North of England.
“Four of these are high-volume pumps capable of moving 1,000 litres of water per second.
“Continuing rain in Wales could also see parts of Herefordshire, Worcestershire and Shropshire experience flooding impacts to land and roads from the River Wye and River Severn.”
Further information is available at www.gov.uk/check-if-youre-at-risk-of-flooding or follow @EnvAgency and #floodaware on Twitter.