A key challenge in the development of magnetic drug targeting (MDT) as a clinically relevant technique is designing systems that can apply sufficient magnetic force to actuate magnetic drug carriers at useful tissue depths. In this study an optimisation routine was developed to generate designs of Halbach arrays consisting of multiple layers of high grade, cubic, permanent magnet elements, configured to deliver the maximum pull or push force at a position of interest between 5 and 50 mm from the array, resulting in arrays capable of delivering useful magnetic forces to depths past 20 mm. The optimisation routine utilises a numerical model of the magnetic field and force generated by an arbitrary configuration of magnetic elements. Simulated field and force profiles of optimised arrays were evaluated, also taking into account the forces required for assembling the array in practice. The resultant selection for the array, consisting of two layers, was then constructed and characterised to verify the simulations. Finally the array was utilised in a set of in vitro experiments to demonstrate its capacity to separate and retain microbubbles loaded with magnetic nanoparticles against a constant flow. The optimised designs are presented as light-weight, inexpensive options for applying high-gradient, external magnetic fields in MDT applications.