It comes as holidaymakers faced massive queues to leave the UK on Friday, with lorries and cars backing up for a second day today.
Former chancellor Mr Sunak said: ‘The situation needs to be urgently addressed by the French.
‘They need to stop blaming Brexit and start getting the staff required to match demand. It’s absolutely not acceptable to have families stranded in their vehicles like this.’
Liz Truss, Mr Sunak’s rival in the leadership race, said today: ‘This awful situation should have been entirely avoidable and is unacceptable.
‘We need action from France to build up capacity at the border to limit any further disruption for British tourists and to ensure this appalling situation is avoided in future.’
But French transport minister Clément Beaune hit back at Ms Truss’s suggestion France needed to fix the ‘avoidable and unacceptable’ situation.
He added: ‘I discussed this constructively with my counterpart [Grant Shapps]. But France is not responsible for Brexit.’
The port’s chief executive Doug Bannister said traffic was moving faster today, after French authorities sent extra passport officers to man all 12 booths at the ferry terminal.
He said: ‘As long as we get the resources we need, when we require it, I am hopeful we will never have a repeat of yesterday [Friday].
‘I don’t know what the cause was for yesterday but they [French officials] certainly recognised the challenge and stepped up today, and for that I’m grateful.
‘Whilst Brexit has impacted the transaction times at the border, yesterday’s events weren’t caused by Brexit.’
But Brexit does mean that Brits travelling to France must have their passports stamped on entry, which means the process of getting in to the country is slower.
In a tweet, Clément Beaune said: ‘The French authorities are mobilised to control our borders and facilitate the traffic as much as possible.
‘I discussed this constructively with my counterpart [Grant Shapps]. But France is not responsible for Brexit.’
Lucy Morton, professional officer for the ISU – the union for borders, immigration and customs staff, was asked on the BBC’s Today programme whether Brexit is to blame for more rigorous checks by French border officials.
She said: ‘It’s certainly the case that the checks are more rigorous than they used to be.
‘Prior to Brexit, there was a deemed right of entry. We weren’t in Schengen but there were still very minimal checks … and frequently there were no French checks at all.’
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