Normal traffic through the tunnel resumed on Tuesday night, according to Eurotunnel, which is in dispute with workers at MyFerryLink who want to prevent the sale of two out of the company's three ferries.
Tuesday's disruption, which also hit the port of Calais, saw some of the roughly 3,000 migrants in the town trying to board lorries whose passage was slowed by the strikers' pickets.
Britain on Wednesday said it would increase screening at Dover and set up task force to hunt down people smugglers.
"It is hugely regrettable that we've seen these incidents occurring as a result of industrial action in France," British Immigration Minister James Brokenshire told the BBC.
"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."
The Nord-Pas de Calais regional council on Wednesday announced that it would contribute 10 million euros to an effort to save the ferries, although Eurotunnel says it has already signed a contract to rent them to Danish compnay DFDS.