Well now that you mention it, yes, the story would also work very well either in the 50s or in the 80s too.
In the 1980s, you'd have the extra advantage of having more sci-fi invasion movies (and TV series - remember V?
to draw inspiration from. Media attention would probably be more important too. That being said, the existence of Star Wars etc. and the way it changed pop culture and the general public's perception of science fiction should also be taken into account.
In the 1950s, you could really thump the Cold War / Red Scare button - and "alien invasion" actually was one of the only themes explored by science-fiction movies back then. And if you play in Britain, well... QUATERMASS was on TV! (or was it Nightshade?
)
Here are some "alien invasion" films from the 1950s that might be used as backdrop (or you could just as well invent your own meta-fictional movie, taking elements from several different sources...
THE DAY THE EARTH STOOD STILL (1951)
THE THING FROM ANOTHER WORLD (1951)
WAR OF THE WORLDS (1953)
INVADERS FROM MARS (1953)
KILLERS FROM SPACE (1954)
INVASION OF THE BODY SNATCHERS (1956)
EARTH vs. THE FLYING SAUCERS (1956)
INVASION OF THE SAUCER MEN (1957) - mmmh do I detect a pattern here?
PLAN NINE FROM OUTER SPACE (1959)