Successful utilization of natural anionic clays like montmorillonite and hectorite for the homogeneous dispersion of multiwalled carbon nanotubes (MWCNTs) in ethylene-co-vinyl acetate (EVA), motivated us to investigate the role of magnesium aluminium layered double hydroxide (MgAl-LDH) in a similar role. MWCNT/MgAl-LDH 3D hybrid filler (HML) was prepared from the unmodified constituents in 1:1 wt. ratio by simple dry grinding method. The dispersion of this hybrid filler with extraordinary stability was subsequently used in the preparation of EVA/HML nanocomposites by solution intercalation method. Analysis shows MWCNTs to be homogeneously dispersed in the polymer matrix in presence of LDH layers. Reinforcing efficiency of HML in EVA matrix was evaluated through detailed studies of the nanocomposites. Mechanical, thermal and dielectric properties of neat EVA are substantially improved with HML content. Maximum improvement observed in tensile strength, elongation at break and toughness are 182%, 87%, and 300% respectively at 4 wt% HML. However, best dielectric response with ~400 and ~89 times enhancement in AC conductivity and dielectric constant are observed 1 wt% HML content. Comparison of HML with previously reported MWCNT/montmorillonite (MMT) and MWCNT/hectorite 3D hybrid fillers confirms superior reinforcing efficiency of the former. Improvements in properties are attributed to homogeneous dispersion of fillers and improved polymer-filler interaction on account of synergy between MWCNTs and LDH.