The yellow (be aware) warning is currently in place until 11am tomorrow (Wednesday January 17).
Earlier today the area affected was the extreme west of West Sussex but this has recently been extended to cover all of the South.of England.
The Met Office says: "Showers are falling as sleet, snow and hail already in the north of the warning area, and this threat spreads to parts of Wales, the Midlands and southern England on Tuesday evening and overnight into Wednesday.
"Delays to travel are possible, with a lower likelihood of cancellations of public transport.
"Some roads and pavements will turn icy, with an increased likelihood of some accidents and injuries. This warning has been extended eastwards across southern England and further into the Midlands."
However, the Chief Forecaster's assessment is: "2-6cm of snow is likely in places, especially on higher ground above 100-200m, where a few places in the Pennines and upland Wales may see more than 10cm. A slushy cover of 1 to 3cm seems more likely at lower levels and closer to the western coasts, as well as across most of southern England, with some areas here seeing very little or no snow."
A further Met Office warning is already in place for strong gusting wind Wednesday evening and into Thursday morning.