We have investigated dielectric, magnetic and magnetodielectric (MD) properties of polycrystalline Y-type hexaferrite Ba2Mg2Fe12O22 (BMFO). Rietveld refinement of x-ray diffraction pattern and hexagonal plate like Field Emission Scanning Electron Microscope (FESEM) micrograph confirms the phase purity with rhombohedral crystal structure (R-3m space group). Magnetization measurement suggests irreversibility in zero field cooled and field cooled data below 270 K whereas opening of hysteresis in isothermal magnetization (M-H plot) indicates weak ferromagnetism. Surprisingly, two distinct dielectric anomalies, near 25 K (TI) and 270 K (TII) are observed in the vicinity of magnetic spin phase transition, suggesting a strong coupling between dielectric and magnetic properties. A confirmation of this magnetodielectric coupling is seen in both temperature as well as magnetic field dependent MD results. In addition, a butterfly loop like switchable MD effect is observed below 200 K which owes to enhanced magnetic ordering and reduced leakage current. Finally, we confirm magnetic field induced MD effect below 200 K may be due to intrinsic coupling between electric and magnetic order parameter whereas above 200 K this effect is due to Maxwell-Wagner space charge polarization. The existence of substantial MD coupling (∼30%) at 15 K is obtained which is exciting and pave the way for further scientific research.