They added that the floodwater could be "fast flowing or deep" with a substantial risk of lightning strikes, hail and strong winds.
The Met Office warned of up to 1.2in (30mm) of rain in one hour and 2in (50mm) in three hours across England, with parts of the eastern coast the only areas not covered by the alert, which runs until the end of today.
The Met Office said the warnings meant "that homes and businesses could be flooded quickly, with damage to some buildings from floodwater, lightning strikes, hail or strong winds".
Northern Rail said several rail services would be replaced by buses because of the flooding, with trains cancelled between Manchester and towns including Wigan and Stalybridge.
People were warned of disruption to transport, with sudden flooding potentially leading to road closures.
Forecasters said that parts of the North West had seen 40mm to 50mm of rain in about 24 hours, with 52.2mm recorded between 11am on Saturday and 11am on Sunday at Greenfield near Oldham.
Weather misery is set to batter the United Kingdom just days after it roasted in a 38.7C heatwave - the hottest since records began.
"There is a slight chance that power cuts could occur and other services to some homes and businesses could be lost".
The Environment Agency has issued six flood warnings across the Midlands, North West, and east of England.
Met Office forecasters say that showers will increase in frequency into the afternoon. Belgium, Germany and the Netherlands also saw records fall.