Mr Ellwood said the suggestion France could have shared knowledge about the Exocet that could have saved British lives “warrants further investigation”.
He added: “We don’t know the wider decision-making that surrounded this. Indeed, those responsible might not even be alive today.
“As we look to future battles we must learn from past events, and that includes how we work with allies and how we share critical intelligence. It certainly would have been game-changing had France chosen to share this characteristic of the Exocet.”
Dr Fox pointed out that in 2010, David Cameron and Nicolas Sarkozy, then the prime minister and French president, signed the bilateral Lancaster House treaties for defence and security cooperation.
“I would have thought in the spirit of those treaties the French would want to be as open and honest as possible with us,” he said. “It would not change anything about that relationship, but it would set the historical record straight.”
Bob Seely, a Tory MP and former Army captain who sits on the foreign affairs select committee, said: “If Exocets contained what was effectively an on/off switch, the French should have shared that with us.
“If it turns out that information was withheld, that would be one of the most shameful episodes in Anglo-French relations. A lot of British sailors died because of those weapons, and we owe it to the families of those who died, and to history, to get to the truth.
“It may be that the French did tell us all there was to know, but we need them to be transparent.”