[en] Tests of general relativity (GR) are still in their infancy on cosmological scales, but forthcoming experiments promise to greatly improve their precision over a wide range of distance scales and redshifts. One such experiment, the Square Kilometre Array (SKA), will carry out several wide and deep surveys of resolved and unresolved neutral hydrogen (H i) 21 cm line-emitting galaxies, mapping a significant fraction of the sky from $0⩽<!--\; ???\; -->z\lesssim <!--\; ???\; -->6$. I present forecasts for the ability of a suite of possible SKA H i surveys to detect deviations from GR by reconstructing the cosmic expansion and growth history. SKA Phase 1 intensity mapping surveys can achieve sub-1% measurements of $f{\mathrm{\sigma <!--\; ??\; -->}}_8$ out to $z\approx <!--\; ???\; -->1$, with an SKA1-MID Band 2 survey out to z ≲ 0.6 able to surpass contemporary spectroscopic galaxy surveys such as DESI and Euclid in terms of constraints on modified gravity parameters if challenges such as foreground contamination can be tackled effectively. A more futuristic Phase 2 H i survey of $\sim <!--\; ???\; -->{10}^9$ spectroscopic galaxy redshifts would be capable of detecting a $\sim <!--\; ???\; -->2\mathrm{\%<!--\; \%\; -->}$ modification of the Poisson equation out to z ≈ 2.