Ding! Dong! Steed calls in on a lady friend - from Look Westward
There has previously been very little written about this Avengers strip.  One, very short, one-page article in Vol. 2 #2 of On Target magazine reprints a page from the strip, and states that it is "a page from an extremely rare Avengers comic strip... the only time that Steed & Mrs Gale appeared in this form.  Look Magazine, May 2nd, 1964."  The only other mention seems to be in issue 21 of Timescreen magazine, a special all-comics edition written by Andrew Pixley.  In it he states that "During the Spring of 1964, ABC's offbeat thriller series The Avengers appeared in a serialised comic form for the first time in the pages of Look magazine.  Very little is known about this publication, aside from the fact that the black and white one-page instalment saw Patrick Macnee's John Steed working alongside Honor Blackman's Mrs. Catherine Gale to battle a computer which aimed to gain power over people via an important television transmission."   In the supplement to that issue, we are told that there are 'six issues' of Look which contain Avengers strips.  In fact, there were ten parts to that particular story, and it wasn't the only story, there were at least another three of varying lengths, and Look magazine was actually Look Westward, which looks like it could have been a Bristol/South West alternative to The TV Times in the same way that TV World was in the Midlands (ABC) region.

Epidemic of Terror
The strips were also published in The Viewer, which I believe was the Scottish alternative to The TV Times and in The Manchester Evening News (which is where I initially tracked them down).  However, this being The Avengers, nothing is ever simple.  The strips in The Manchester Evening News were printed every Saturday in a single block format, starting in February 1964 and concluding in September of that year.  The Look Westward strips (the first two of which have been forwarded to me by Geoff Barlow - take a bow) are one and a half pages per issue, except for the 'The Computer Menace', which was one page per issue according to the reprinted page in Stay Tuned.

This makes the debut of the strip in Look Westward and in The Viewer as September 14th 1963, and its conclusion in those magazines as May 9 1964.  The original published order of the strips is, theoretically, this: September 14 to October 19 1963: 'Epidemic of Terror', November 2 to December 7 1963: 'Quest For A Queen', December 21 1963 to February 1 1964: 'Operation Harem' and March 7 to May 9 1964: 'The Computer Menace'.  This chronology works on the assumption that there were week-long gaps between the second and third and third and fourth stories as there had been between the first and second stories - the dates for the 'The Computer Menace' strip hinge upon the date of the reprinted page in Stay Tuned being correct.
I've used the stories that I have the best copies of too make the following pages.  The name of the publication which sits at the very top is the one which I've used.  When I have better copies of The Manchester Evening News strips or all the Look strips then I'll switch to just the one.  In the meantime, go here:

The Avengers newspaper strip - full details