I remember the show , and I found a copy of it - but it's not a very good copy.
I found out what it was! It was a British series called "Ghost Story"and the episode in question is called "The Exorcism"
According to what little information I have it aired on one of the BBC Radio stations - that's all of the information I have about this show. Sorry I couldn't get more information about it.
See if this is the story here:http://www.dumb.com/oldtimeradio/listen/12808/Drama_British_Shows_2/British_Shows_2/Ghost_Story_The_Exorcism.html
PS: I noticed that you original post was back in December, but since I wasn't here to help you then, I hope it will still be of use to you.
Since the last time I updated this, I found out more about the author and story. The Exorcism was written by Don Taylor. He passed away in 2003. The information about him (from his obituary from the British Theatre Guide) is this:
Writer and director Don Taylor has died after a long battle against cancer. Best known as the writer of The Roses of Eyam, a play telling how the villagers of Eyam in Derbyshire shut themselves off from the outside world when they discovered the plague amongst them and so prevented it spreading to near-by communities, a play which is now a GCSE set text, he worked in both television and theatre.
His most recent work was The Road to the Sea at Richmond's Orange Tree Theatre from 19th February to 15th March this year, the theatre in which his Women of Troy, his version of Euripides' The Trojan Women, played in 2001. The first professional production of any of his plays onstage was in 1967, when the Edinburgh Traverse premiered Grounds for Marriage. This was followed by Sisters (1968) at the Northcott, Exeter, and Sam Foster Comes Home (1969) at the Glasgow Citizen's Theatre.
His writing for television included The Theban Plays (1984) (Oedipus the King, Oedipus at Colonnus and Antigone), When the Actors Come (1978), a BBC2 Play of the Week, and A Last Visitor for Mr Hugh Peter (1981). He both wrote and directed these, and also directed Find Me (Omnibus, 1974); For Tea On Sunday (1978), another Play of the Week; In Hiding (1980), for BBC2 Playhouse; The Crucible (1980) and Two Gentlemen of Verona (1983). A stage version of Oedipus the King was produced by the National Youth Theatre in 1998.
He was also the author of Directing Plays.
He began his career in 1960 when he joined the BBC and worked almost exclusively over the next four years with NJ Crisp, David Turner, Hugh Whitmore, and David Mercer. In 1963 there were major artictic differences between him and the newly appointed Head of Drama Sydney Newman and left when his contract expired. He returned as a freelance director in 1964 and 1965, after which he claimed he was blacklisted by the BBC Drama department and it was not until 1972 that he again returned to direct his own plays The Exorcism and, the following year, The Roses of Eyam.
He worked for the independent station ATV in 1974 and 1976.
You can find out more on this link from wikipedia:http://en.wikipedia.org/wiki/Don_Taylor_%28director%29
A version of this story (The Exorcism) was included in part of the TV series "Dead of Night" (1972). The first radio broadcast of the story was in done in 1992 and this is also available as a play.