Britain is demanding that Argentina pay back £45m in loans that the country took out from the UK in order to buy ships and helicopters later used to invade the Falkland Islands.
The figures were uncovered by the Jubilee Debt Campaign, which lobbies governments to forgive countries' loans taken out by its former dictators.
But UK Export Finance, a branch of Vince Cable's business department, said it has "no plans to offer debt forgiveness" to Argentina for the loans it completed in 1979.
Buenos Aires' £45m debt includes loans for two British made Type-42 Destroyers and two Lynx helicopters, which were used in the 1982 invasion of the Falklands.
Nick Dearden, director of Jubilee Debt Campaign, said the decision to lend the military junta money to buy British weapons, made by the then Labour government, was "illegitimate and odious".
"The newly uncovered documents show that then foreign secretary David Owen knew the UK government was lending money for arms to an abhorrent regime," he said.
"This is not the only occasion in which debt has been run up supplying arms to a regime which British soldiers would soon be fighting.
"The anniversary of the Falklands War should force the government to question the way it does business. Business Minister Vince Cable must implement Liberal Democrat policy and stop subsidising war through the backing of loans to other governments to buy weapons."
He added: "The Liberal Democrats must stick to their pledge to rule invalid loans recklessly given to dictators."
In an Autumn 2010 policy paper the Lib Dems said they would seek to rule "invalid" any past lending that was "recklessly given to dictators known not to be committed to spend the loans on development".
The hefty loans taken out during Argentina's military junta era contributed to the economic crisis it suffered in 2000.
Relations between the UK and Argentina have been tense for months in the lead up to the 30th anniversary of the Fallklands War.
Britain has pledged to defend the territory from any renewed aggression, while Argentina has renewed its claim to the islands, which it calls the Malvinas.