The combined influence of shape anisotropy, dipolar interactions and exchange bias (EB) on the magnetization reversal of arrays of NiFe and NiFe/IrMn sub-micrometre elliptical magnetic elements has been investigated using magneto-optical Kerr effect microscopy and micromagnetic modelling. An applied field during film growth resulted in exchange fields around 50 Oe for the unpatterned films, micrometre sized stripes and nanomagnet arrays. High aspect ratio single-layer ellipses reverse via a single-domain-like switching while low aspect ratio structures reverse through the movement of a vortex core. The vortex formation and annihilation fields for closely spaced elliptical elements depend on the inter-element spacing and the aspect ratio. In particular, the stability range of the vortex state is lower for more strongly interacting or higher aspect ratio structures. On the other hand, a modest EB can significantly increase the stability of the vortex states and promote single-domain states that lead to different remanent configurations. A combination of EB, shape and inter-element spacing can therefore be used to tailor the behaviour of coupled nanomagnet arrays.