A yellow-level warning is in place between 4am and 11am tomorrow, with some dense fog and freezing patches forming in the early hours of the morning.
This means drivers should expect slower journey times and some delays to bus and train services are possible.
The weather warning is in place for Portsmouth and Hampshire, as well as most of the south of the UK.
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A Met Office spokesperson said: ‘Visibility could be less than 100m in places across parts of England and east Wales on Tuesday morning.
‘Whilst the fog is expected to gradually lift and thin during the morning some patches could persist until lunchtime in the east.’
The Met Office said Monday night would be cold and frosty for many areas and could be the coldest night across the UK as a whole.
Locally, temperatures could drop as low as minus 9C (15.8F) in rural Scotland and minus 7C (19.4F) in parts of England and Wales.
A Met Office spokesman said the current cold spell may soon come to an end, with temperatures recovering throughout the week.
Public Health England (PHE) has also issued a cold weather warning from 9am on Monday until 12pm on Wednesday.
Dr Emer OConnell, a consultant at PHE, advised people to look out for anyone who may need help staying warm.
‘Older people and those with heart and lung problems are at risk of getting sick in cold weather,’ she said.
There is a cloudy outlook to this week’s weather forecast in Portsmouth with temperatures remaining chilly, although there is a slim chance of rain.