An alien spaceship lands in rural England. One of the inhabitants wanders off and in front of a car. Taking his ''funny clothes'' to be fancy dress, the driver (now minus his mistress, one of those nice little touches that grounds the story) take him to the local hospital for treatment.
The staff, led by Dr Mike Vernon (the ever-dependable Edward Judd), soon realise that their patient is not of this earth, beginning with a blood sample that does not look normal and followed by the discovery of a metal disc in the man's head. Meanwhile, two other (female) aliens search for their missing compatriot and soon track him down to the hospital, which is then discovered to be sealed off from the rest of the world by an invisible barrier...
The aliens, later designating themselves as Lystrians, all look Oriental, though any racist subtext to this is rendered less likely by the casting of Tsai Chin as one of the hospital nurses and, as such, a fully integrated member of the local and by extension national communities. Moreover, before the alien's true otherness is revealed, her character is also asked if the alien man is Chinese or Japanese, but she does not think he is -- there is something not quite right and she's never seen clothes like his before; all very much contra the racist cliche “They [we] don't all like alike”
Edward Judd, Tsai Chin and the alien
More importantly, the Invasion title itself is actually somewhat misleading, insofar as the aliens are more concerned with their own matters than earthly ones, namely the recapture of an escaped prisoner (or two).
The film's writer, Robert Holmes, had earlier worked on Dr Finlay's casebook and would later become a prominent contributor to Dr Who. It is easy to see Invasion as a combination of the two. The hospital setting equates to the Earth-centred 'base under siege' scenario that were becoming especially common during Patrick Troughton's tenure as the Time Lord. More directly, other aspects of the story prefigure the introduction of Jon Pertwee in the Holmes-scripted Spearhead from Space, as the newly regenerated Doctor is taken to hospital and it gradually becomes apparent that he is not human, although the other aliens there are more predictably malign and actually intent on invasion. Beyond this, there are also UNIT-like military men, an unsympathetic, narrow-minded man from the government, and a competent pre-Liz Shaw female scientist. (The film as a whole has an unusual, if sometimes more obviously pre-feminist, take on gender issues.)
Fans of the Quatermass (E)xperiments or Terence Fisher's Planet triumvirate, especially the slightly later Night of the Big Heat (Island of Terror also starred Judd), will also find much that is comfortably familiar and oh-so-very particularly British. In other words, while the special effects aren't up to much this is somewhat beside the point: Rather, it's about the ideas, the performances, and the generation of an atmosphere of unease.
They don't make them like this anymore, more's the pity...