Today has been cold mostly everywhere, with maximum temperatures below 10°C and overcast conditions with some showers and snow at the medium height.
On Tuesday, the easterly winds will cause still cold conditions and there will be some showers, especially in England, with snow possible at low levels (notice the 528 dam in Figure1 on the south of England).

During the night some showers are expected on eastern England and Scotland (snow on the hills), moving westwards during the day (showers possible also in Wales, Northern Ireland and southern England). However, the most important precipitation should be observed in England (North and east). Depending on the intensity of the precipitations, some snow might be possible at low-levels in southern England and Wales between the afternoon and evening. However, it will be wet snow (due to positive temperatures) and it will be difficult to see snow accumulation in the lower areas, instead few centimeters can be expected on the hills.
The temperatures will decrease, especially in southern England, with little difference between minimum and maximum values. In the morning (2-7°C) mostly everywhere, with the lowest values observed in southern England, Wales and highlands. In the afternoon, values between (4-8°C) with the lowest temperatures still observed in southern Egland and Wales (where snow at low levels is possible). Still, due to the positive temperatures (and precipitation not too intense), it’s likely to see only snowflakes at low levels.
Finally, the winds will be easterly over the UK, moderate on the east of England and on the Irish Channel (25-35 mph).