Multiferroic BiFeO3 (BFO), La/Co modified BiFeO3 (BLFO/BLCFO) ceramics prepared by solid state reaction route were characterised and their magneto-dielectric properties were investigated. The phase purity of La/Co modified BFO ceramics was confirmed from powder X-ray diffraction studies and distortion observed in the lattice due to compression was found to be associated with polarization switching on La/Co co-substitution into BFO. An enhancement and stability in saturation magnetization with low coercive field (Hc ≈ 400 Oe) has been achieved at room temperature in La/Co modified BFO samples. Dielectric and impedance measurements reveal the enhanced values of dielectric constant, real and imaginary part of impedance and modulus on account of modification by La/Co in BFO. The modulus studies confirm the presence of ionic polarization due to the co-substitution of La2+/Co3+ ions and dominant grain effects in BLFO and BLCFO samples. The magneto-dielectric effect (% MDE) is found to be maximum value of 1.8 in magnitude at 8 kOe for BLFO-10%Co, and increases with increase in Co content in to BLFO. The substitution of Co into BLFO generates polarization at La and Fe layer, which provides the enhanced value of %MDE and stability in purity of BFO ceramic.