This paper presents a new sample of BL Lac objects selected from a deep (30mJy) radio survey of flat spectrum radio sources (the CLASS blazar survey). The sample is one of the largest well-defined samples in the low-power regime with a total of 130 sources of which 55 satisfy the 'classical' optical BL Lac selection criteria, and the rest have indistinguishable radio properties. The primary goal of this study is to establish the radio luminosity function (RLF) on firm statistical ground at low radio luminosities where previous samples have not been able to investigate. The gain of taking a peek at lower powers is the possibility to search for the flattening of the luminosity function which is a feature predicted by the beaming model but which has remained elusive to observational confirmation. In this study, we extend for the first time the BL Lac RLF down to very low radio powers ~10^22^W/Hz, i.e. two orders of magnitude below the RLF currently available in the literature. In the process, we confirm the importance of adopting a broader, and more physically meaningful set of classification criteria to avoid the systematic missing of low-luminosity BL Lacs. Thanks to the good statistics we confirm the existence of weak but significant positive cosmological evolution for the BL Lac population, and we detect, for the first time the flattening of the RLF at L~10^25^W/Hz in agreement with the predictions of the beaming model.