The tunnel had to be shut yesterday when the workers broke in and migrants attempted to board UK-bound lorries.
Migrants were seen this morning today at the side of the motorway in Calais while others were seen opening the back doors on lorries stuck in traffic.
All tunnel services had to be suspended for several hours yesterday.
But today Eurotunnel said that its passenger and freight shuttles were running as scheduled through the tunnel while high-speed train company Eurostar was operating a full service from London through the tunnel to Paris and Brussels.
The ferry workers’ action closed the port of Calais for a time yesterday, but the port was open today and Dover-Calais sailings were operating normally.
Eurotunnel spokesman John Keefe said today: “After we resumed services yesterday, we ran an enhanced freight service through the night to clear the backlog.
“We are systematically searching every truck that comes into the terminal on the French side to ensure it is clear of migrants before it enters the tunnel.”
Eurostar had to cancel all services from mid-afternoon until the end of the day yesterday, but services started on time today with the 5.40am, London to Paris train the first to depart.
Large queues built up at Eurostar’s London terminal at St Pancras station yesterday.
A Eurostar spokeswoman said today: “We provided dinner and a hotel room for a number of people last night. Our trains are full today and everything is running smoothly.”
However, Vanessa Magdelyns, 33, from Brussels, said she and “at least 50” people had spent the night at St Pancras.
She said: “I laid down to rest but there was no sleeping. It was too cold. We didn’t get any blankets. When they saw that we were staying here overnight they could have helped us.”
She was due to get the 5pm train to Brussels yesterday but is now booked on a service later today.
More resources will be put into screening arrivals at Dover, Immigration Minister James Brokenshire has said, adding that extra French police officers are being deployed in Calais to deal with the problem.
The travel problems yesterday come amid a worsening migrant situation near the Port of Calais where numbers camped there have swelled to more than 3,000 since April.
Aid workers have reported a “catastrophic” situation, with predictions that some 2,000 more migrants displaced from war-torn countries including Eritrea, Syria and Afghanistan could arrive over the summer.
Mr Brokenshire told the BBC: “It is hugely regrettable that we’ve seen these incidents occurring as a result of industrial action in France.
“We are putting additional resourcing into the port of Dover to enhance screenings and detections there so that we’re looking at this on both sides of the Channel.”
He added: “We have been advised the French authorities are sending further policing to deal with law and order issues, and we will be keeping in close contact with them in the hours ahead.”
The deputy mayor of Calais, Philippe Mignonet, yesterday reiterated calls from French politicians for the border to be moved from northern France to Britain.
Mr Brokenshire said: “These deployments of additional border force resourcing at Coquelles around the Eurotunnel terminal and also from our work at Calais, buttressed by further support at Dover, is about maintaining that safety and security and the integrity of the border, which is our absolute focus.”