ABSTRACT Fanaroff–Riley type II (FR II) low-excitation radio galaxies (LERGs) are characterized by weak nuclear excitation on parsec-scales and properties typical of powerful FR IIs (defined as high-excitation radio galaxies, hereafter HERGs/BLRGs) on kiloparsec-scales. Since a link between the accretion properties and the power of the produced jets is expected both from theory and observations, their nature is still debated. In this work, we investigate the X-ray properties of a complete sample of 19 FR II-LERGs belonging to the 3CR catalogue, exploiting Chandra and XMM–Newton archival data. We also analyse 32 FR II-HERGs/BLRGs with Chandra data as a control sample. We compared FR II-LERG and FR II-HERG/BLRG X-ray properties and optical data available in literature to obtain a wide outlook of their behaviour. The low accretion rate estimates for FR II-LERGs, from both X-ray and optical bands, allow us to firmly reject the hypothesis as they are the highly obscured counterpart of powerful FR II-HERGs/BLRGs. Therefore, at least two hypothesis can be invoked to explain the FR II-LERG nature: (i) they are evolving from classical FR IIs because of the depletion of accreting cold gas in the nuclear region, while the extended radio emission is the heritage of a past efficiently accreting activity; and (ii) they are an intrinsically distinct class of objects with respect to classical FR Is/FR IIs. Surprisingly, in this direction, a correlation between accretion rates and environmental richness is found in our sample. The richer the environment is, the more inefficient is the accretion. In this framework, the FR II-LERGs are intermediate between FR Is and FR II-HERGs/BLRGs both in terms of accretion rate and environment.