Sleet and snow showers were expected overnight in parts of north-west and south-west England, the Midlands, and Wales.
Wet conditions and snowmelt could also cause icy patches to develop in the morning, with the yellow warning set to stay in place until 10:00 GMT.
In Scotland, similar conditions are likely to affect areas including Strathclyde, the Highlands, Aberdeenshire, and the Northern Isles, with snow accumulation of five to 10cm expected in higher areas.
The current warning expires at midday.
For many there will be single-figure temperatures along with dry conditions and some sunshine expected through the rest of Tuesday.
In Northern Ireland, rain, sleet, and snow was expected to continue overnight on Monday, with a warning of snow and icy patches set to remain until 11:00.
Almost 200 flood warnings – including one severe warning – and some 300 flood alerts were in place across England as of 05:00 on Tuesday.
The warnings mostly apply to parts of Worcestershire, Warwickshire, Leicestershire, Nottinghamshire, Lincolnshire, and Peterborough, with parts of Cheshire, Yorkshire, and the south coast also affected.
The severe warning – indicating significant disruption and danger to life – applies to part of the River Soar near the village of Barrow upon Soar in Leicestershire, where a number of caravan parks were evacuated Monday.
The Environment Agency said flooding of homes in the village was expected to continue and river levels were set to remain high until Wednesday.
