The structural, phonon, magnetic, dielectric, and magneto dielectric responses of the pure bulk Brownmillerite compound Ca2FeCoO5 are reported. This compound showed giant magneto dielectric response (10%-24%) induced by strong spin-lattice coupling across its spin reorientation transition (150-250 K). The role of two Debye temperatures pertaining to differently coordinated sites in the dielectric relaxations is established. The positive giant magneto-dielectricity is shown to be a direct consequence of the modulations in the lattice degrees of freedom through applied external field across the spin reorientation transition. Our study illustrates novel control of magneto-dielectricity by tuning the spin reorientation transition in a material that possess strong spin lattice coupling.