A calculation of the one-loop self-energy and vacuum-polarization corrections to the hyperfine splitting of the 1s and 2s states in light H-like ions is carried out to all orders in the parameter Zα. Using the known values for the Zα-expansion coefficients, the numerical data obtained are extrapolated from Z=5 and higher to Z=0, 1, and 2, with the resulting accuracy being significantly better than in previous evaluations. Our calculation shifts the theoretical value of the normalized difference of the 1s and 2s hyperfine-structure intervals in He+3 by 0.056kHz and improves its accuracy.