There may be poor visibility in some areas.
Wrexham is again covered in the weather warning, which is the second to be issued in two days.
Chief forecaster Andy Page said it will thicken over the next few hours and warned to expect rush-hour travel problems.
"Fog will persist in some parts of Northern Ireland during Thursday afternoon, thickening up towards dusk with the visibility falling below 100 metres in places".
The met office added: "There is a small chance that power cuts will occur and other services, such as mobile phone coverage, may be affected".
The warning, which was originally issued at 2am this morning, now runs until 2am Friday morning and is in effect for the entire country.
The warning covers Northern Ireland, Wales, north-west England, south-east England, West Midlands, Yorkshire and Humber and south-east England. Lowest temperatures 4 to 8 C.
"Now we have ideal conditions for widespread fog across the country, particularly, for some southern areas, where it could linger for some lengthy periods from tonight".
Where is radiation fog in the United Kingdom?
On its website, the Met Office says: "The cooling of land overnight by thermal radiation cools the air close to the surface".
"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".
"Elsewhere it will be dry with clearer spells". Some patches of fog will form and also some frost.
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