Most Galactic globular clusters (GCs) harbour multiple populations of stars (MPs) that are composed of at least two generations: the first generation is characterised by a standard α-enhanced metal mixture, as observed in field halo stars of the Milky Way, and the second generation displays an anti-correlated CN-ONa chemical abundance pattern in combination with an enhanced helium fraction. Adequate collections of stellar spectra are needed to characterize the effect of these changes in the stellar abundance on the integrated light of GCs. We present a grid of synthetic stellar spectra to cover the atmospheric parameters relevant to old stellar populations at four subsolar metallicities and two abundance patterns that are representative of the first and second generations of stars in GCs. The integrated spectra of the populations were computed using our stellar grid and empirical stellar populations, namely, colour-magnitude diagrams from the literature for Galactic GCs. The spectra range from 290 to 1000 nm, where we measured the effect on several spectrophotometric indices due to the surface abundance variations attributed to MPs. We find non-negligible effects of the MPs on the spectroscopic indices that are sensitive to C, N, Ca, or Na, and on the Balmer indices; we also describe how MPs modify specific regions in the near-UV and near-IR that can be measured with narrow or medium photometric passbands. The effects vary with metallicity. A number of these changes remain detectable even when we account for the stochastic fluctuations due to the finite nature of the stellar population cluster.