It has been the stoic philosophy, especially in the guise of the publications of Garve, Baumgarten, and Wolff:
Kant did not need
Garve’s translation to remind him of the Stoic principle, which was still
popular with eighteenth-century thinkers like Wolff and Baumgarten;
and the other variants [of the categorical imperative] are hardly directed against Cicero. (Timmermann, J. (Ed.). (2009). Kant's' Groundwork of the Metaphysics of Morals': A Critical Guide. Cambridge University Press, p. xxviii)
This makes also clear that Kant did not want to argue against popular moral philosophy (i.e. its content - he was critical of its methods): he rather considered the categorical imperative to be the (implicit) basis of it.
Kant's own reference to "popular moral philosophy"
What popular moral philosophy meant for Kant is further elaborated by Timmermann at a later point in his text: it refers to Garve in particular (who recently had published both a translation of Cicero's De officiis and a book that could be seen as a comment to it) in at least one case, here in a comment to Ak. 4:409.20:
One is reminded of Cicero’s De officiis and Christian Garve’s
Philosophische Anmerkungen und Abhandlungen, both equally eclectic and
riddled with historical examples. It is difficult to believe that at least
the present attack on contemporary popular moral philosophy was not
inspired by Garve’s 1783 twin publications. (ibid:56)
The understanding that it is Garve in particular (and not Baumgarten and Wolff) is further supported by Allison:
As the title suggests, it [i.e. the second section] is concerned with
the two approaches to moral philosophy in relation to which Kant largely framed his
project in GMS: the universal practical philosophy, which was initially formulated by
Wolff and further developed by Baumgarten and the latter's student Georg Friedrich Meier, and the eclectic “popular moral philosophy,“ which was associated with
Christian Carve, as well as figures in the Berlin enlightenment. (Allison, H. E. (2011). Kant's Groundwork for the Metaphysics of Morals: a commentary. OUP Oxford, p. 37)