The effect of cold high pressure densification (CHPD) on anisotropy of the critical current density (Jc) in « in situ » single core binary and alloyed MgB2 tapes has been determined as a function of temperatures at 4.2 K, 20 K and 25 K as well as at applied magnetic fields up to 19 T. The study includes binary and C4H6O5 (malic acid) doped MgB2 tapes before and after CHPD. It is remarkable that the CHPD process not only improved the Jc values, in particular at the higher magnetic fields, but also decreased the anisotropy ratio, Γ = Jc///Jc┴. In binary MgB2 tapes, the anisotropy factor Γ increases with higher aspect ratios, even after applying CHPD. In malic acid (C4H6O5) doped tapes, however, the application of CHPD leads only to small enhancements of Γ, even for higher aspect ratios. This is attributed to the higher carbon content in the MgB2 filaments, which in turn is a consequence of the reduced chemical reaction path in the densified filaments. At all applied field values, it was found that CHPD processed C4H6O5 doped tapes exhibit an almost isotropic behavior. This constitutes an advantage in view of industrial magnet applications using wires with square or slightly rectangular configuration.