It is urging people to check their flood risk and remain prepared to take action as the situation changes.
There are ten flood warnings in place across Yorkshire - meaning flooding is expected - and 19 flood alerts.
There are no flood warnings for the Aire around Leeds, but further afield there are flood alerts Lower and Upper River Nidd, the Lower River Wharfe and the Tidal River Wharfe and Tidal River Ouse from Naburn Lock to Selby.
There is also a Met Office yellow weather warning for rain on Friday, Saturday and Monday for much of Yorkshire.
England has already received 141 per cent of its average February rainfall so far with some areas experiencing a month’s worth of rain in 24 hours.
River levels continue to exceed existing records across the country, including the Colne, Calder and Aire.
Since the start of Storm Dennis, over 1,000 Environment Agency staff have been mobilised to operate flood defences and temporary pumps, clear debris from rivers and inspect damaged flood defences.
Caroline Douglass, Director of Incident Management at the Environment Agency, said: “Flooding has a long lasting and devastating impact on people’s lives, and our thoughts remain with all those who have been flooded.
“Further spells of rain in northern England from Friday and into the weekend may lead to further significant river flooding, particularly across the Pennines, while ongoing river flooding remains probable for the lower Severn for the remainder of the week.
“This is the third weekend we have seen exceptional river levels and stormy weather, and with the effects of climate change, we need to prepare for more frequent periods of extreme weather like this.
"People need to be aware of their flood risk, sign up to flood warnings, make a flood plan and not to drive or walk through flood water.”
The public can keep up to date with the latest safety advice, call Floodline on 0345 988 1188.
The flood warnings for Yorkshire (as of 4pm, Thursday)
Low lying properties in the Upper Hull catchment
River Aire at Birkin
River Aire at Hirst Courtney
River Aire at Hirst Marsh and West Marsh
River Ouse at Bishopthorpe
River Ouse at Naburn Lock
River Ouse at York - Fulford and Fordlands Road
River Ouse at York - riverside properties
River Ouse at York - Skeldergate and Tower Street
River Ouse at York - St George`s Field and Queen`s Staith