The first capped Test, a thrilling encounter, took place in 1981 and since then England and the Pumas have a long shared history.
It was a long time coming, but when England and Argentina first met in a capped international match, it proved worth the wait.
The first official Test match between the two took place on Saturday 30 May, 1981, and it was a thriller, with a late Clive Woodward try denying the hosts a symbolic victory.
That game, though, was far from the first time the two countries' paths had crossed on a rugby field. Their shared history goes back much further.
In the late nineteenth century, when rugby football first began to flourish, Britain and Argentina were closely linked by trade and the presence of a large ex-pat community in Buenos Aires.
Affluent Brits brought with them the sports they played at home. While soccer grew most rapidly, rugby found a place among the English-speaking professional classes.
In 1910, the RFU decided to send a touring team to Argentina. Some referred to it as an 'England' team, but the three Scottish members of the squad would have had something to say about that.
The 'Combined British' team, as their hosts called them, were captained by England fullback John Raphael - the first Jewish player to be capped by England - and won their match against Argentina by 28 points to 3.
Though the link with England began to dwindle in importance after the Second World War, it remained in certain forms. It was embodied - literally - in Barry Holmes, who represented both countries in the single year of 1949 and remains the only man to do so.
Argentinian rugby went from strength to strength as the years progressed, though an encounter with England still eluded them.
A proposed tour to play the Pumas in 1973 was cancelled due to terrorist threats, with England organising a last-minute trip to New Zealand instead. That quirk of history led to the famous 'White Tornadoes' win in Auckland - the first ever victory by an England team on Kiwi soil.
In 1978, England met the Pumas at last. As Argentina was not yet a member of the International Rugby Board, the hosts could not award caps for the match, but it was a near full-strength England team that met the tourists at Twickenham.
The Pumas, led by legendary fly-half Hugo Porta, confounded expectations to run the home side dangerously close in a match that was drawn 13-13.
Argentina would not have to wait another 68 years for their next crack at the English. The RFU organised a two-Test tour there for the summer of 1981.
From the beginning it was clear that this was to be no summer holiday. Touching down in Buenos Aires shortly after dawn, the players were met by torrential rain, lightning, flooded roads - and an immediate training session. 'Just a loosener', remarked Mike Davis, the England coach.
This being an amateur rugby tour, they did of course find some time to enjoy themselves. Argentine hospitality was particularly generous. After a warm-up victory over a Northern Selection XV, the post-match barbecue lasted until three in the morning. 'It's the only time I've ever made a post-match speech on the day after the game', said skipper Bill Beaumont.
After four tour matches came the first Test. This time, thanks to a change in International Board rules, England were allowed to award caps. The two nations were finally meeting in a fully capped match.
England had been favourites three years earlier but many were backing the Pumas ahead of the game in Buenos Aires.
England handed debuts to Tony Swift on the wing, Steve Mills at hooker and John Fidler in the second row. The Leicester trio of Dusty Hare, Clive Woodward and Paul Dodge added experience in the backs.
The England pack made an impressive impact in the first half, and Cambridge student Huw Davies, England's fly-half, scored a try to give the tourists the lead.
By the hour mark the Pumas had hit back to build a 10-4 lead, but England kept the pressure on. Teenage fullback Daniel Baetti spilled a high ball under the posts, and Woodward pounced to score. Hare converted to level things, but soon after a second try for Puma wing Marcelo Campo pegged back the tourists once more.
A frantic final quarter ensued. First, Dusty Hare sent over a long penalty to cut the lead to three. Then, Puma scrum-half Tomas Landajo - father of the current Pumas number 9 Martin Landajo - dropped a goal to take Argentina to a 19-13 lead with just minutes remaining.
Was this to be their first ever triumph against England?
Sadly for them, it was not. With just four minutes left on the clock, Scott pinched an Argentine lineout throw and the ball was fed to the backs. Dodge cut open the defence and the Leicester man fed his club partner Woodward to go in under the posts.
Hare's conversion levelled the match at 19-19 - another ding-dong battle, another draw.
According to Peter West of the Times, it was 'a just and honourable result', and one 'against the odds' for the English.
Bolstered by their performance, England won the second Test 12-6 to take the series. Even considering the many highlights in his career, Beaumont remembered this as his finest win in an England shirt. '[We were] the first England team to ever to win over there. Winning in the England jersey in games like that was special,' he has said.
The Pumas' maiden victory against England would eventually come in 1990, in Buenos Aires. Their first, and only, victory at Twickenham came 16 years later. This Saturday, they'll be looking for their second. What price the draw?