Before the Screaming Begins (1977) is a good start: our central characters, Tom and Sally Harris, are celebrating their wedding anniversary with a walk in the woods when he is abducted by aliens. Sally is frustrated when the police refuse to believe her, but then Tom is returned with new strange powers and a message from the aliens for the people of Earth, and it turns out similar appearances and disappearances have happened simultaneously all over the world; we get mixed up with the Prime Minister (Patrick Troughton, doing a brilliant impression of Harold Wilson) and sinister official A.P. Smith (played by Donald Hewlett, the only main cast member to appear in all three plays).
The Silent Scream (1979) is I think the best of the three, and has interesting foreshadowing of Torchwood: Children of Earth - so much so that I wonder if RTD has acknowledged it as source material? - though of course The Midwich Cuckoos/Village of the Damned is probably a common root. Lots of creepy children endowed with super powers (one played by Susan Sheridan who was the original Trillian at about the same time), and the government pondering extreme measures to deal with them. No Patrick Troughton this time, but Hannah Gordon takes over as Sally Harris.
With a Whimper to the Grave (1984) has the best cast but weakest plot of the three. Patrick Troughton takes back the role of Prime Minister, but loses the election to "Marge", played by Angela Thorne (not her only such role). Timothy West is a chief alien. Maureen "Vicki" O'Brien takes over as Sally. But the central character is Donald Hewlett's A.P. Smith, who links between the aliens' revelation of What They Were Really Up To, and the authorities' attempt to neutralise the alien threat. Unfortunately the to plot strands confuse rather than reinforcing each other, and the wipe-out-the-alien-menace bit is very poorly paced (and there is a very irritating character called Geoffrey Palmer, which must be an in-joke). However you'll want to listen to it for completeness if you've heard the first two.