More than 100 flights have been cancelled and The Met Office has released a warning to drivers, urging them to prepare for hazardous conditions on roads.
The yellow “be aware” warning applies to London, the south-west, the south east and some eastern parts of the country.
The fog is expected to be at is heaviest until 10.30am.
Travellers were advised to check their flight's status before leaving home.
The UK has been gripped by freezing fog as temperatures dip below freezing
Flights have also been cancelled due to the harsh weather conditions.
Heathrow has cancelled 100 flights and London City Airport has cancelled ten. Meanwhile Stanstead does not have any delays.
A Stansted Airport spokeswoman said there had not been any cancellations, but advised passengers to check with their airlines for the latest information and allow enough time to get to the airport.
Steven Keates, a weather forecaster, said: “In this area we are likely to see some dense, freezing fog patches developing, particularly through the early hours, which could impact some travel through the course of tomorrow’s rush hour.
Drivers have been warned to beware of dense fog and frost
“There will be difficult driving conditions and delays at some airports, including the London airports.”
Mr Keates added: "We ask everyone to be aware of the potential impact the fog will have on the roads.
"Take it steady, allow a bit of extra time for your journey.
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"If you have got an early morning flight it might be worth double checking, just to make sure there are no delays at the airport."
A message on the Heathrow website said: "Heathrow advises passengers to check their flight status with their airline before coming to the airport.
"Heathrow's top priority is the safety of passengers and we apologise to those whose travel has been affected."
Drivers have been warned of 'difficult conditions' on roads
Temperatures dipped to their lowest in Katesbridge, Northern Ireland, where minus 6.9C (20F) was recorded.
Meanwhile, in England a low of minus 6.2C (21F) was recorded in Northolt, around 10 miles from Heathrow.
Temperatures in London plunged to -7.4C overnight.
Over the course of the day, temperatures are not expected to rise above zero and cool weather will persist throughout the week.
The fog may persist throughout the week
Mr Keates said : “On Tuesday, we’re expecting another frosty start with temperatures not getting much higher than 4C or 5C.
"There will be another risk of fog which could be more extensive.
"It will either become thicker if it has failed to clear on Monday night or we will see it reappearing.”
More to follow…