We investigate the age and metallicity distributions of bright globular clusters (GCs) in the candidate intermediate-age early-type galaxies NGC 3610, 584 and 3377 using a combination of new Gemini’s Near InfraRed Imager and Spectrometer K′-band imaging and existing optical VI photometry from Hubble Space Telescope data. The V−I versus I−K′ colour–colour diagram is found to break the age–metallicity degeneracy present in optical colours and spectroscopy, as I−K′ primarily measures a population’s metallicity. In addition, it is relatively insensitive to the effect of hot horizontal branch (HB) stars that are known to be present in massive old GCs. By interpolation between simple stellar population model tracks, we derive photometric cluster ages, metallicities and masses. In general, we find that ‘metal-poor’ GCs with [Z/H] ≲−0.7 dex are older than more metal rich GCs. For the most massive GCs () in NGC 3610 with available spectroscopic data, the photometric ages are older by ∼2 Gyr, and this difference is more pronounced for the metal-poor GCs. However, the photometric and spectroscopic metallicities are in good agreement. We suggest that this indicates the presence of a hot HB in these massive clusters, which renders spectroscopic ages from Balmer line strengths to be underestimated. To support this suggestion, we show that all Galactic GCs with feature hot HBs, except 47 Tuc. Using a recent observational relation between the luminosity of the most massive GC and the galaxies’ star formation rate (SFR) at a given age, we find that the galaxies’ peak SFR was attained at the epoch of the formation of the oldest (metal-poor) GCs. The age and [Z/H] distributions of the metal-rich GCs are broad, indicating prolonged galaxy star formation histories. The peak ages of the metal-rich GCs in the sample galaxies NGC 3610, 584 and 3377 are 3.7, 5.9 and 8.9 Gyr, respectively. The peak value of the age and metallicity distributions of the GCs is correlated with the host galaxies’ luminosity-weighted age and metallicity, respectively, indicating that the GCs can indeed be used as relevant proxies of the star formation histories of galaxies.