The warning predicts snow for Scotland, parts of northern England, and much of Wales.
The forecaster is warning of “heavy snow” with the potential to cause “significant disruption” on Thursday and Friday.
This is what the Met Office are expecting: “Snow could develop quite widely across the warning area on Thursday and Friday as a potentially quite deep area of low pressure moves across the UK.
“Parts of Northern Ireland, north Wales and northern England are currently expected to see the worst of the conditions on Thursday, with parts of Scotland and northern England then seeing the heaviest snow on Friday.
“Event totals could bring 5 to 10 cm of snow to many locations, even at low elevations, with potentially 15 to 20 cm accumulating across the northern portion of the warning area. Higher elevations of the North Pennines, Southern Uplands, higher parts of the Central Belt and the southern Highlands may see as much as 30 to 40 cm of snow in places.
“In addition, there is potential for strong winds, which may lead to blizzard conditions and drifting of lying snow.”
Warnings of snow are also in place further south on Wednesday.
Met Office Deputy Chief Meteorologist Steven Keates said: “The impactful weather will continue through the second half of the week as mild air meets cold air with further snow, ice, wind and then rain likely later in the week and into the weekend.
“From Wednesday, the focus of further snow is across parts of southern England and south Wales, with snow likely to lower levels for a time, and many may wake up to a couple of centimetres of snow on Wednesday morning.
“Through Thursday and Friday the snow risk spreads to central and northern areas of the UK, though it’s not possible to pick out precise locations regarding who will see the heaviest snowfall. With a developing situation, it’s important to stay up to date with the latest forecast and further warnings are very likely.”
Ice will be an additional hazard for many through the week, with sub-zero temperatures creating some hazardous travel conditions. Temperatures could drop as low as -15°C overnight on Tuesday in some sheltered Scottish Glens, especially where there’s fresh snow cover.
The UK Health Security Agency has issued a Level 3 Cold Weather Alert for the whole of England which is likely to be reviewed in the coming days.
Dr Agostinho Sousa, Head of Extreme Events and Health Protection at the UK Health Security Agency, said: “During periods like this, it is important to check in on family, friends and relatives who may be more vulnerable to the cold weather, as it can have a serious impact on health.
“If you have a pre-existing medical condition or are over the age of 65, it is important to try and heat your home to at least 18°C if you can.’’