It has issued a yellow ‘be aware’ warning saying up to 3cm of snow could fall across the area.
The Met Office said: “Showers of sleet and snow will continue to affect many eastern and particularly northeastern parts of the UK through the rest of Tuesday and into Wednesday giving icy stretches on untreated surfaces.
“Rain and sleet is more likely near exposed coasts but slightly further inland local snow accumulations of 1-3cm are possible above around 100m, with perhaps 5-10 cm over the Grampians and North York Moors.
“The public should be aware of the potential for disruption to travel.”