Composite materials with engineered band gaps are promising solutions for wave control and vibration mitigation at various frequency scales. Despite recent advances in the design of phononic crystals and acoustic metamaterials, the generation of wide low-frequency band gaps in practically feasible configurations remains a challenge. Here, we present a class of lightweight metamaterials capable of strongly attenuating low-frequency elastic waves, and investigate this behavior by numerical simulations. For their realization, tensegrity prisms are alternated with solid discs in periodic arrangements that we call 'accordion-like' meta-structures. They are characterized by extremely wide band gaps and uniform wave attenuation at low frequencies that distinguish them from existing designs with limited performance at low-frequencies or excessively large sizes. To achieve these properties, the meta-structures exploit Bragg and local resonance mechanisms together with decoupling of translational and bending modes. This combination allows one to implement selective control of the pass and gap frequencies and to reduce the number of structural modes. We demonstrate that the meta-structural attenuation performance is insensitive to variations of geometric and material properties and can be tuned by varying the level of prestress in the tensegrity units. The developed design concept is an elegant solution that could be of use in impact protection, vibration mitigation, or noise control under strict weight limitations.