The South East and south-west have also been issued with warnings.
Other parts of the UK will face a risk of flooding.
More rain is expected across much of southern England, south Wales and south-west Scotland, along with thunderstorms and squally winds, forecasters predict.
The Environment Agency has issued more than 20 flood alerts and motoring organisations are urging drivers take extra care in wet weather.
Gareth Harvey, a forecaster with MeteoGroup, the weather division of the Press Association, said: "The rain and strong gusts of wind will hang around throughout the morning before the showers ease off to the east, with sun coming from the west."
