The weather warning is one of the longest ever issued, spanning from today until next Friday, 2 March.
Commenting on the outlook for Monday to Wednesday in the south east, a Met Office spokesman said: "Extremely cold with snow showers becoming more widespread and also heavier, especially Monday night onwards".
A blast of cold weather dubbed the "Beast from the East" is approaching and is expected to bring the coldest spell of the winter from Monday.
As the week progresses the cold weather is expected to move to northernly parts of the United Kingdom including Northern Ireland.More news: Special Olympic athletes play for the pure love of the game
Temperatures are not expected to reach over 0C during the day by late next week as the cold snap takes hold.
Met Office meteorologist Martin Bowles said: "The feels-like temperature will be 5C lower than what we see on the thermometer because of a strong easterly wind chill".
"We haven't had temperatures that low in late February since 2013".
Cold with highest temperatures of 6 to 8 degrees in a moderate southeast wind.
Following sunny spells over the weekend, the Arctic front will dominate from tomorrow night.More news: Chris Lynn not to undergo surgery after dislocating shoulder
The cold snap will affect the whole of the United Kingdom from Sunday night with temperatures expected to drop to -8C in some areas.
"As a result, the increased likelihood of a cold spell of weather has been forecast for many days, but there is now greater confidence about the time scale and also the extent of snowfall".
Up to 10cm of the white stuff is possible on both days, even down to low levels, but some areas may only have a couple of centimetres or even nothing at all.
"Sunday will be a dry and sunny day".
"And it is certainly looking cold into the rest of the week, with temperatures of 2-3C (35-37F), with sharp nighttime frosts".More news: After Florida Shooting, Sponsors And Partners Ditch US Gun Lobby Group