A severe weather warning has been issued for Yorkshire, including Leeds and Sheffield.
It means visibility on the roads could be less than 100 metres in places.
A spokesman for The Met Office said: "Areas of fog, including some locally dense freezing fog patches with visibility less than 100 metres, will readily form on Monday evening and persist through the night into Tuesday. Please be aware of likely tricky road travel conditions.
With little cloud and light winds fog is expected to readily develop during Monday evening, affecting the evening rush hour in some areas as well as the morning rush hour on Tuesday. Fog is then expected to be locally slow to lift and clear on Tuesday, lingering for much of the morning and perhaps onwards into the afternoon in some spots."