The Met Office says in addition to icy stretches, which are likely to cause difficult travel conditions, people should be cautious about the danger of slips and falls, which could cause injuries.
The warning covers the whole region, as well as the east of Scotland to the north and down to Cambridgeshire in the south.
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The warning states: “Icy patches are expected to develop, especially on untreated surfaces, with showers feeding in from east coasts leaving surfaces wet.
"There is also the chance of some freezing rain, mainly for northeast England, overnight into Tuesday.
"Further snow is also likely mostly for hills above 200m to 300m.
“Some small accumulations are possible with southeast Scotland and northeast England most at risk.
"Here 2cm to 5 cm is possible in places above 300m and 10cm above 400m though ice looks likely to be the main hazard.”
The forecast specifically for the region today says there will be sunny spells and scattered showers, occasionally wintry over high ground though perhaps becoming less frequent this afternoon.
It will feel bitterly cold in the northeasterly breeze. with a maximum temperature 4C.
Tonight the Met Office expects it to be “bitterly cold” with further showers of rain, sleet and snow, these especially wintry over high ground.
Icy patches are likely and winds will become light away from coasts.
The temperature could drop to -4C.
Further ahead, tomorrow will be another day of sunny spells and showers, these likely to be wintry over high ground and perhaps briefly to low levels.
It will also be cold with icy patches and a northeasterly breeze and the maximum temperature will be 4C.
The longer term forecast, from Wednesday to Friday, is that there will be sunny spells and wintry showers on Wednesday and cloudy on Thursday, with rain and snow.
It will be brighter with wintry coastal showers on Friday, but becoming increasingly cold with sharp frosts and icy patches.