Nearly the whole of Northern Ireland, and the west of England, including Liverpool, Manchester, Wolverhampton, Bristol and parts of Devon will also be affected by thick fog. Overnight fog and any frost should clear.
The warning, which was originally issued at 2am this morning, now runs until 2am Friday morning and is in effect for the entire country.
Mark Wilson, a forecaster at the Met Office, told MailOnline: 'We have issued a fog warning with parts of Northern Ireland, Wales, the west of England and Devon affected.
Temperatures are expected to remain low climbing no higher than 4C in the northwest but slightly warmer temperatures of 7C in London and the southeast.
Tomorrow will be another cloudy and murky day across the country with more of the same forecast through the week. Afternoon temperatures will range from 5° to 9°, while it will be coldest in the north.
On its website, the Met Office says: "The cooling of land overnight by thermal radiation cools the air close to the surface".
Where is radiation fog in the United Kingdom?
"This results in a reduction of the air's ability to hold moisture which allows water vapour to condense into tiny water droplets eventually leading to the formation of fog".
WeatherOnline forecaster Simon Keeling added: "Further spells of drizzle here expected for the far northeast of Scotland tonight".
He said: "It happens when you get clear skies and it cools down and you get fog patches forming out of these skies".