The Fermi satellite discovery of the gamma-ray emitting bubbles extending 50 deg (10 kpc) from the Galactic Centre has revitalized earlier claims that our Galaxy has undergone an explosive episode in the recent past. We now explore a new constraint on such activity. The Magellanic Stream is a clumpy gaseous structure passing over the South Galactic Pole (SGP) at a distance of at least 50-100 kpc. Patchy H-alpha emission discovered along the Magellanic Stream over the SGP is a factor of 5 too bright to have been produced by the Galactic stellar population. Time-dependent models of Stream clouds exposed to a flare in ionising photon flux show that the ionised gas must recombine and cool for a time interval 0.6 - 2.9 Myr for the emitted H-alpha surface brightness to drop to the observed level. A nuclear starburst is ruled out. Sgr A* is a more likely candidate because it is two orders of magnitude more efficient at converting gas to UV radiation. The central black hole (4 x 10^6 Msun) can supply the required ionising luminosity with a fraction of the Eddington accretion rate (3-30%). In support of nuclear activity, the H-alpha emission along the Stream has a polar angle dependence peaking close to the SGP. Moreover, it is now generally accepted that the Stream over the SGP must be further than the Magellanic Clouds. At the lower halo gas densities, shocks become too ineffective and are unlikely to give rise to a polar angle dependence in the H-alpha emission. Thus it is likely that the Stream emission arose from a `Seyfert flare' that was active 1-3 Myr ago, consistent with the cosmic ray lifetime in the Fermi bubbles. Sgr A* activity today is greatly suppressed (70-80 dB) relative to the Seyfert outburst...