Structural inversion asymmetry controls the magnitude of Rashba spin-orbit coupling in the electron energy spectrum of a narrow band gap semiconductor. We investigate this effect for a series of two-dimensional electron gases in In0.52Ga0.48As quantum wells, surrounded by In0.52Al0.48As barriers, where either one or two electric subbands are populated. Structural inversion asymmetry does not exist at low carrier density while at higher carrier densities (above (4–5) × 1011 cm−2), a finite spin splitting is observed. The spin orbit coupling coefficients (α) are determined from the power spectrum of the oscillatory magnetoresistance, although this is complicated by magnetointersubband scattering in the region where two subbands are occupied. In the lowest subband, α1 ≈ (0.6–1.0) × 10−11 eV m over a range of (4–9) × 1011 cm−2 total carrier density. In the second subband, α2 ≈ 2.2 × 10−11 eV m, and this reduces with increasing carrier density. The spin-orbit coupling effect disappears at high carrier density although a strong structural inversion asymmetry still exists. We discuss these results with the consequences for spintronic devices operating on the principle of charge density dependent or electric field dependent spin manipulation in narrow band gap semiconductors.