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Grids of zero-age horizontal branch (ZAHB) models are presented, along with a suitable interpolation code, for −2.5 ≤ [Fe/H] ≤ −0.5, in steps of 0.2 dex, assuming Y  = 0.25 and 0.29, [O/Fe] = +0.4 and +0.6, and [ m /Fe] = +0.4 for all of the other α-elements. The HB populations of 37 globular clusters (GCs) are fitted to these ZAHBs to derive their apparent distance moduli, (m − M) V . With few exceptions, the best estimates of their reddenings from dust maps are adopted. The distance moduli are constrained using the prediction that (M F 606 W − M F 814 W )0 colours of metal-poor, main-sequence stars at |$M_{F606W} \mathrel {\rm{{\gt }\lower.5 ex\rm{\sim }}}5.0$| have very little sensitivity to [Fe/H]. Intrinsic (M F 336 W − M F 606 W )0 colours of blue HB stars, which provide valuable connections between GCs with exclusively blue HBs and other clusters of similar metallicity that also have red HB components, limit the uncertainties of relative (m − M) V values to within ±0.03–0.04 mag. The ZAHB-based distances agree quite well with the distances derived by Baumgardt & Vasiliev. Their implications for GC ages are briefly discussed. Stellar rotation and mass loss appear to be more important than helium abundance variations in explaining the colour–magnitude diagrams of second-parameter GCs (those with anomalously very blue HBs for their metallicities). [ABSTRACT FROM AUTHOR]