Temperatures in the north will be 8C at their highest, with the south-west enjoying slightly higher temperatures of 12C. Frost and icy patches will develop also. Towards evening, rain will develop in the west.
Half term for many parents and children will be a washout as Britain is set to be battered by heavy rain and snow for most of next week.
Wednesday morning will be wet with rain and sleet, heavy at times.
Showers and blustery weather is forecast for the north-west, where the highest temperatures us expected to be around 5C, with the south-west's at about 7C.
On Sunday night, wintry showers will continue with accumulations of snow in places.
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A spokesman said: "A very cold westerly airstream will bring frequent snow showers to many western and central areas on Sunday".
Frosty and snowy showers will give predicted accumulation of 3 cm of snow, with a larger amount of snowfall expected on mountainous areas and on higher ground. Lowest temperatures will range from -3°C to 0°C.
Public Health England forecasters have extended a cold weather health alert until Tuesday.
Temperatures in the city and county are expected to fall to zero tonight, paving the way for an icy start to Friday, with snow likely as it struggles to reach three degrees. Overnight temperatures will be as low as -3°C to 0°C.
"Next week, the weather will remain in its changeable phase, going between milder and colder spells with further spells of snow". Rain and strong southerly winds will spread overnight.