We report on our further analysis of the expanded and revised sample of potential BL Lac objects (the 2BL) optically identified from two catalogues of blue-selected (UV excess) point sources, the 2-degree field (2dF) and 6-degree field (6dF) quasi-stellar object (QSO) Redshift Surveys (2QZ and 6QZ). The 2BL comprises 52 objects with no apparent proper motion, over the magnitude range 16.0 < bJ < 20.0. Follow-up high signal-to-noise spectra of 36 2BL objects and near-infrared (NIR) imaging of 18 objects, together with data for 19 2BL objects found in the Sloan Digital Sky Survey (SDSS), show 17 objects to be stellar, while a further 16 objects have evidence of weak, broad emission features, although for at least one of these the continuum level has clearly varied. Classification of three objects remains uncertain, with NIR results indicating a marked reduction in flux as compared to SDSS optical magnitudes. Seven objects have neither high signal-to-noise spectra nor NIR imaging. Deep radio observations of 26 2BL objects at the Very Large Array (VLA) resulted in only three further radio detections; however none of the three is classed as a featureless continuum object. Seven 2BL objects with a radio detection are confirmed as candidate BL Lac objects, while one extragalactic (z= 0.494) continuum object is undetected at radio frequencies. One further radio-undetected object is also a potential BL Lac candidate. However, it would appear that there is no significant population of radio-quiet BL Lac objects.