The value of the spatial separation between electric and magnetic fields in an electromagnetic wave is fundamentally constrained by the nonlocal nature of Maxwell's equations. While electric and magnetic energy densities in a plane wave propagating in vacuum are equal at each point of space, carefully designed photonic structures can lead to a spatial separation of the electric and magnetic fields. Here, a set of high-index dielectric tubes was proposed and demonstrated to deliver a record high spatial separation overcoming the free space scenario by more than three orders of magnitude. The separation effect in the structure is enabled by the near-field interference between an incident radiation and anapole-type states designed by tuning geometrical parameters of coupled dielectric tubes. Near-field scanning of field components within the void structure confirmed the predicted values of magnetoelectric separation. Furthermore, the near-field interference concept in application to magnetoelectric separation can be employed in a range of spectroscopic tests, where objects (e.g., atoms with magnetic optical transitions) can be placed in voids. Devices providing tunable separation between the fields are important in nano-optics for magnetic particle or atom detection and trapping, in medicine for magnetic resonance imaging, etc.