Eurotunnel is drawing up plans to improve security at its French terminal to combat a predicted increase in the numbers of people risking their lives to try to stow away on trains bound for the UK.

Speaking on Thursday after the company’s financial results showed a one-third drop in the number of freight trains using the Eurotunnel, the company’s chairman and chief executive Jacques Gounon said an extra 1,000 people a month had arrived in Calais since June.

“We had a manageable situation until June and then the number of migrants in Calais increased incredibly every month,” he said. “Now officials recognise that there are as many as 6,000, and it could well increase.”

The company has stepped up security at the terminal over the summer with 18 miles of fencing that will be completed later this month, and hundreds of extra security staff and police funded by both the UK and French governments.

Last month Peter Sutherland, the United Nations special representative on migration, said he was sickened by the conditions in “the Jungle”, the refugee camp on the outskirts of Calais, and called on the UK and France to open a permanent centre in the port that would allow people wanting to claim asylum in Britain to have their cases heard without risking their lives.

Gounon agreed that increasing security on its own would not solve the problem.

Eurotunnel grew its overall business in the third quarter with revenue 3% higher than last year, at €334.4m. Gounon said it was a good performance in difficult circumstances.

“It proves we have a robust business model and we are able, whatever the difficulties, to provide the quality of service requested,” he said.

He said the drop in the number of freight trains was due to people trying to get on to trains near the terminal, but insisted it was “very marginal” to Eurotunnel’s overall business.

Thousands of people who are fleeing war and persecution in the Middle East and east Africa are living in appalling conditions on the outskirts of Calais.

After security was improved around the ferry port earlier this year, those who wanted to get to the UK attempted to hide in lorries queuing to get into the Eurotunnel terminal a few miles outside Calais, or tried to jump directly on to moving trains.

At the height of the disturbances, more than 1,000 attempts a night were being made by people trying to stow away on trains bound for the UK.

“The completion of fences is a significant step,” said Gounon. “We are anticipating an increase number of migrants around the port of Calais and going to the tunnel, which is why we are preparing a new action plan with a series of steps to protect the tunnel. Unfortunately those talks are ongoing so I cannot disclose the measures we intend to implement.”

At least 16 people have died trying to get to the UK since June, including children and young people. Hundreds more have been injured. “It is very sad and each time it creates a significant emotion within our staff,” said Gounon.

He said Eurotunnel was doing all it could to prevent people putting themselves at risk, distributing leaflets to warn the migrants about the dangers of people trying to get to the UK via the tunnel

“People do not understand the risks they are taking when they run on tracks,” he said.