David Cameron has promised to “do everything we can” to ease the disruption in Calais as a man was killed when 1,500 migrants tried to enter the Channel tunnel on Tuesday night.

The death, the eighth since the start of June when the crisis at the French port started escalating, came a night after 2,000 migrants tried to enter the tunnel. The man, whom French media said was of Sudanese descent, was reportedly hit by a lorry.

Speaking in Singapore during a Southeast Asian trade trip, the British prime minister said “there’s no point trying to point fingers of blame”.

“It’s about working with the French, putting in place these additional security measures, adding in the investment where that’s needed — Britain will always come forward with that,” he said.

Mr Cameron added: “I have every sympathy with holidaymakers who are finding access to Calais difficult because of the disturbances there and we will do everything we can to work with the French to bring these things to a conclusion.”

Theresa May, the home secretary, will chair a meeting of the government’s Cobra emergency committee to address the issue.

The Home Office has said that £7m of additional funding was paying for 1.2 miles of new fencing at the Eurotunnel site at Coquelles. The extra fencing, which was used to secure the Nato summit in Wales last year, is due to be completed this week.

It is part of efforts to create a “secure zone” to protect UK-bound lorries from migrants.

Tim Woolrich, of the Calais Migrant Solidarity charity, said people were “dying on a regular basis now”. “Every single day I see people coming back from that stupid border with bad injuries,” he said.

Last year there were 800 migrants living in squalid makeshift housing in Calais. Today there are thought to be as many as 5,000, reflecting the sharp rise in people desperate to leave war-torn countries such as Syria and Libya, and to escape repression in places such as Sudan and Eritrea.

There were 19,000 attempts to cross the Channel in the year to June, double last year, according to the Home Office.

Migrants’ tactics for trying to reach the UK seemed to have changed, Mr Woolrich said, with those in the camp now attempting to storm the Eurotunnel complex en masse. This was largely because of the new security measures, he suggested.

“It’s the new fence that’s the problem,” he said. “How do you pull a fence down? You pull a fence down with a lot of people.”

Ms May said France had also promised extra resources to bolster security at Calais.

When asked why British taxpayers should be paying for a problem taking place on French soil, she said: “We have juxtaposed controls at the border. We work together on dealing with this particular problem.”

The government is also looking at ways of using foreign aid in the countries of origin to discourage people from leaving.