The government is holding an emergency Cobra meeting to discuss how to bolster border security in Calais, after migrants took advantage of strikes by French ferry workers this week to try to illegally board lorries bound for the UK.

The meeting of cabinet ministers and senior officials will be chaired by Patrick McLoughlin, the transport secretary, as the prime minister is in Brussels for the European council, where leaders are expected to discuss the migrant crisis in the Mediterranean, linked to the growing camps in Calais.

Ministers are already considering sending more resources to Calais, including extra border officials and sniffer dog teams, as well as strengthening fences around port and rail crossings.

Police have reopened parts of a motorway in Kent that was closed for 36 hours to ease congestion. The Channel tunnel was closed because of the strike action on Tuesday, leading to long delays and disruption for travellers and lorry drivers.

Police had advised motorists to seek alternative routes, with only specially ticketed HGVs allowed to travel on the road. On Thursday Kent police said the coastbound M20 between junctions eight and nine was now open to all traffic.

Don Armour, the Freight Transport Association’s international manager, said closures were now a frequent occurrence, and the strike had merely exacerbated intolerable pressure already faced by drivers crossing through Calais.

“Drivers were unable to open their windows or leave their vehicles for fear of either being threatened or would-be stowaways getting on board,” he said. “Numbers of migrants at the port have increased from a few hundred to around 3,000 and we are hearing every day from members whose trucks have been damaged, drivers have been threatened and deliveries have been compromised. This situation can’t be allowed to continue.”

There have been unconfirmed reports in France that 350 migrants crossed to the UK during this week’s strike and its aftermath.

More than 1,000 police officers remain in the town following the week’s disturbances, including five units of France’s body-armoured riot police – at least 350 officers, according to the prefecture of Calais.

Another 200 officers are around the town, bolstered by 35 riot police officers and 10 officers from the French anti-criminality brigade (BAC) to combat antisocial behaviour in the centre.

In the UK, on Wednesday, David Cameron described the scenes in Calais as “totally unacceptable” but moved to calm tensions with the French by promising to work more closely with them and calling for an end to finger-pointing over who would be to blame.

He said during prime minister’s questions that Britain had to also tackle people-smuggling gangs in north Africa and do more to make Britain a less attractive place for migrants.

David Bolt, the independent chief inspector for borders and immigration, said he would be looking at whether the government was doing enough to create a “hostile environment” for illegal migrants.

In his inspection plan Bolt said he would also be examining how the Home Office used intelligence to stop illegal entrants. “’The effective and efficient working of the UK’s border and immigration functions continues to be of great interest to those responsible for delivering these functions, to parliament, and to the public, not least because we are all touched by them,” he said.

On Tuesday the mayor of Calais, Natacha Bouchart, told French radio that the UK government had “not offered a penny” to help her town ease the pressure caused by the increasing number of migrants arriving en route to Britain.