It has mainly been advocated by English biblical scholars. It is named for Austin Farrer, who wrote On Dispensing With Q in 1955, but it has been picked up by other scholars including Michael Goulder and Mark Goodacre.
The Farrer theory has the advantage of simplicity, as there is no need for hypothetical sources to be created by academics. Instead, advocates of the Farrer theory argue, the gospel of Mark was used as source material by the author of Matthew. Lastly, Luke used both of the previous gospels as sources for his gospel.
In an era when systematic theology had largely become divorced from biblical analysis, Farrer challenged form and source criticism's fragmentation of the gospels by proposing that the evangelists be treated as authors rather than editors.
The Q hypothesis is not, of itself, a probable hypothesis.
Farrer identified Deuteronomy as the inspiration of Luke's design for his teaching section and argued that the composition of the latter was less problematic than others had claimed.