We　have　measured　the　flexophotovoltaic　effect　of　single　crystals　of　halide　perovskites　MAPbBr3　and　MAPbI3,　as　well　as　the　benchmark　oxide　perovskite　SrTiO3.　For　halide　perovskites,　the　flexophotovoltaic　effect　is　found　to　be　orders　of　magnitude　larger　than　for　SrTiO3,　and　indeed　large　enough　to　induce　photovoltages　bigger　than　the　band　gap.　Moreover,　we　find　that　in　MAPbI3　the　flexophotovoltaic　effect　is　additional　to　a　native　bulk　photovoltaic　response　that　is　switchable　and　ferroelectric-like.　The　results　suggest　that　strain　gradient　engineering　can　be　a　powerful　tool　to　modify　the　photovoltaic　output　even　in　already　well-established　photovoltaic　materials.