Officials said only passengers and drivers with advance bookings will be able to travel this morning, while car drivers in the town should only be using lane two.
Some people reported being stuck in queues in Dover for more than five hours overnight, while lorries were queued up along the M20 as staff and police attempted to take control of the situation.
Elsewhere, the rail network is still recovering from yesterday’s major delays on the west and east coast mainlines.
Services from Euston were suspended due to a fallen overhead wire in the Watford area, while Kings Cross trains were affected by a fallen tree near Newark in Nottinghamshire.
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There are likely to be last dashes to major railway stations today, with hubs such as Paddington, which serves Wales and southwest England, closing down on Sunday (Christmas Eve) for engineering works.
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Eurostar trains to resume after strike
Storm Pia also disrupted air travel, with some planes diverting from northern airports and British Airways grounding two dozen flights.
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Video showed a pilot fighting to land his plane at Birmingham in 50mph crosswinds.
The aircraft was less than 100ft from the tarmac when it was forced to pull up – but it made it down safely on the second try.
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Plane struggles to land in Storm Pia
Road traffic is expected to peak later today, with those who want to be driving home for Christmas fighting for space on the tarmac with commuters and shoppers.
The M25 will be a major hotspot, particularly the junctions for the M3 and the M40, while travellers on the M1 and M6 could also be facing long queues.
The RAC advises travellers to avoid the road network between 11am and 6pm today in an effort to avoid standstills.
National Highways said it was removing more than 1,000 miles of roadworks on England’s motorways and major A roads, meaning more than 98% of its network should be free of roadworks until 2 January.