Greaves' 1961 transfer from AC Milan to the Lane - for the then costly sum of £99,999 - risked breaking Britain's strict currency controls which limited the amount of money which could be taken out of the country.
The case even reached the desk of Selwyn Lloyd, the then Chancellor of the Exchequer in Harold Macmillan's Tory government, amid fears of an outcry from outraged football supporters if the deal was blocked.
However, papers released to the Public Record Office show ingenious Treasury officials got round the rules to protect Britain's foreign currency reserves by arguing Greaves should be treated as an "invisible" import or "luxury goods".
William Clowser, an official in the Treasury, explained why he had recommended that the Bank of England should approve the payment for Greaves, who had originally joined Milan from Chelsea for £80,000.
"The transfer fee paid by one club to another for a player's release represents the means by which the paying club secures his services and skill, which are of course of little value except as a member of a football team," he wrote.
"This is closely analogous to a royalty payment which might be made by an industrial concern for the use of a patent or know-how.
"I have told the Bank that, on this justifiable analogy, they may approve the application if it should be made. We would no doubt run into trouble if it were refused."
Another official agreed with the argument that Greaves - the leading English striker of his day - should effectively be counted as an "invisible" import, "however Irish that may appear".
Nevertheless, the issue was sufficiently sensitive that the junior Treasury minister Anthony Barber felt he needed to write personally to Lloyd to explain the decision.
Jimmy Greaves' return to English football with Spurs after a spell in Italy was almost blocked by Treasury officials, according to official files made public for the first time.