We use co-homogeneity one symmetries to construct new families of instantons over Riemannian manifolds with special holonomy groups and asymptotically conical geometry. In doing so, we give a complete description of the behaviour of Calabi-Yau instantons and monopoles with an SU(2)²-symmetry, by considering gauge theory on the smoothing and small resolution of the conifold, and on the canonical bundle of CP¹×CP¹, with their known asymptotically conical co-homogeneity one Calabi-Yau metrics.

Furthermore, we classify SU(2)³-invariant G₂-instantons on the spinor bundle of the 3-sphere, equipped with the asymptotically conical co-homogeneity one G₂-metrics of Bryant-Salamon, and show that if any non-invariant instanton shares the same asymptotic behaviour, its deformation theory must be obstructed.