Newly-released official documents show that while Conservative ministers believed the prospect of such a sporting clash would be "unacceptable" to their own party, they did not want to pick up the bill if the football authorities were left out of pocket.
England, Scotland and Northern Ireland all qualified for the 1982 World Cup finals held in Spain, with the opening game of the tournament scheduled for the middle of June.
Among the papers released by the National Archives at Kew, west London, is a report by environment secretary Michael Heseltine, written in May 1982 as the taskforce steamed towards the Falklands, warning that British and Argentine players could soon be facing each other on the football pitch.
But while Mr Heseltine, as the Cabinet minister responsible for sport, acknowledged that a match involving one of the home countries against Argentina would be a distasteful prospect, he argued it would be wrong to call for a boycott.
Withdrawal by the UK teams would, he said, be greeted as a "moral victory" by the Argentinians while damaging relations with Spain where there was strong support for the Argentine cause. And then there was the cost.
"The financial consequences of a withdrawal are considerable," he wrote.
"There could be a ban on competing in the 1986 World Cup; a heavy FIFA fine; the possibility of compensation; the cancellation of travel and accommodation arrangements; and players' contracts would have to be met.
"The Scottish and Northern Ireland Football Associations could be bankrupted."
In the event, the Argentines surrendered as the tournament began, and all sides were eliminated without playing each other.