Dubbed the “entente frugale” by wags and criticised by some as a dangerous dilution of military sovereignty, Franco-British defence cooperation is nonetheless growing stronger.

Shrinking budgets, a less indulgent United States and Europe’s diminishing military clout in the world have bolstered the two countries’ determination to work together.

That contrasts with the prickly relations between French and British politicians, who have come to blows in recent months on everything from taxes to the European Union budget.

“While the politicians may trade barbs, defence knows there’s nowhere else to go other than working closely together,” said James Arbuthnot, head of the British parliament’s Defence Select Committee.

“At the defence level the cooperation and friendships are more than cordial, they are warm,” he said, joking that he had forgiven France for killing an ancestor at Trafalgar.

But there have been hiccups in the complex business of bringing Europe’s two biggest militaries together.

Britain has in recent weeks helped France with logistics in Mali, where French forces are battling Islamist rebels, but senior military officials had to step in when British pilots refused to carry French ration packs containing matches.

“So what? You can’t carry matches or lighters on British military planes. I think we can work around that,” said a French military official, speaking on condition of anonymity.

“There’s no question how strong our military ties are. There is no questioning the need for strong defence cooperation, everyone’s convinced of that on both sides of the channel.”