Prime Minister David Cameron said he would send more members of the military to assist families caught up in the post-Christmas chaos after he hosted a conference call of the government's COBRA emergency committee.
Nearly 250 flood warnings and alerts are in place in England and Wales, 24 of them severe, signalling a risk to life. The army has already been deployed to help tackle the floods in some areas.
Further rain is expected Sunday, although it is not expected to be as severe as the damage caused by Storm Eva on Saturday.
"More troops are being deployed as part of a plan to do whatever is needed," Cameron wrote on Twitter after the COBRA call to discuss what he said was "unprecedented" flooding.
The latest floods come three weeks after another part of northern England, Cumbria, was badly hit by Storm Desmond.
Some 3,500 properties in York are at risk of flooding and special centres have been set up to allow residents to shelter.
Flood waters in some streets had almost totally submerged parked cars and members of the emergency services were paddling around in dinghies checking for stranded residents.
With its cobbled streets and timbered buildings, York is one of Britain's top tourist attractions. It has a rich history dating back to Roman times and is home to one of Europe's finest cathedrals, which is about 800 years old.
Lisa Pallister, 36, said she decided to leave her home in York with her family as the flood waters rose.
"We didn't think it would reach us because we're raised off the ground and have three storeys but, by this morning, it was on the steps and it is going to rise by lunchtime. So we had a boat ride out," she said.
Hundreds of people have also been evacuated elsewhere in Yorkshire and Lancashire. Parts of the city of Leeds and Greater Manchester are among the places affected by the flooding.
Over 6,000 homes in Greater Manchester and Lancashire were also without electricity due to flood damage.
Manchester police say they are now in the "recovery" phase of their operation, trying to return life to normal for local residents, but warned that this could take some time.