Much of England is included in the warning with forecasters saying the worst-hit areas are likely to be in the Pennines and North Wales.
"Delays or cancellations are likely to rail and air travel".
Travel delays are possible and there is a chance of power cuts throughout the duration of the weather warning. That is the low confidence part of the warnings, keeping it at Yellow but the impacts could be high for Thursday morning.
It is in place until 5am and strongest winds are expected to transfer eastwards before clearing by mid morning.
Power cuts and other services may also be affected, the warning states. This warning has been updated with the southern boundary extended further south over northern England.
"A slushy cover of one-or-two centimetres seems more likely at lower levels and closer to the western coasts, some areas seeing very little or no snow".
"Across parts of the north, a spell of persistent and perhaps heavy snow may develop".
The largest accumulations of snow will be over high ground, with more than 10cm building up above 200 metres.
The Moffat Mountain Rescue Team was called to drivers in Lanarkshire, who were stuck in their cars on the M74 on Tuesday after the heavy snowfall.
Very strong winds will affect parts of the United Kingdom during Wednesday (January 17) night and into Thursday. "The high winds forecast for later in the week may also see some bridge restrictions".
Despite a lack of snow, it was bitterly cold and windy in southern parts of the United Kingdom, with ice expected and temperatures unlikely to go above -1C in London on Tuesday night.
"The location of the most damaging winds is still uncertain, although parts of northwest England and north Wales now look most likely".
Tomorrow will see the rain clearing from southeast England during the morning, leaving the whole United Kingdom with strong winds and blustery showers.
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