Roland Hinterhölzl (2009) Information Structure and Language Change p. 177 (via Google Books):
Roman scribes would usually operate by "copying texts in scriptio continua – that is, without separating words or indicating any pauses within a major section of text (Parkes 1993: 10). Separation by spaces ﬁrst appears in the Insular area (see Saenger 1997: 84-99). It is then used in the Carolingian period (see Müller 1964: 35, Bischoff 1986: 229, Saenger 1990); Parkes (1993: 31) discusses several cases in which Carolingian scribes copying older manuscripts introduced separation. However, spaces were not yet used in a consequent manner (see Saenger 1997: 100): in Carolingian minuscule manuscripts "space was present, but not consistently between every word" (Saenger 1997: 32). Saenger (I997: 32) refers to this kind of separation as "aerated script" (as opposed to "word separation" proper). In central and southern Germany "scribes, after the mid-ninth century, began to write Latin in intensely aerated script, sometimes approaching separation, and began to develop modes for writing the vernacular that were clearly stimulated by Anglo-Saxon models." (Saenger 1997: 102). It is notable that "only at the Abbey of Saint Gall, one of the larger Continental colonies of Irish and Anglo-Saxon monks, did the evolution of text format go so far as to continue consistent emulation of Insular word separation." (Saenger 1997: 103). The Vocabularius Sancti Galli, a Latin-Old High German dictionary, provides an early example of Continental word separation (see Saenger 1997: 103).
A whole book on the topic (with a surprising twist) is the one repeatedly cited above, Paul Saenger (1997) Space Between Words: The Origins of Silent Reading.