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(abridged) We investigate biases in cluster ages and [Fe/H] estimated fromthe (V-K)-(V-I) diagram, arising from inconsistent Horizontal Branchmorphology, metal mixture, treatment of core convection between observedclusters and the theoretical colour grid employed for age and metallicitydeterminations. We also study the role played by statistical fluctuations ofthe observed colours, caused by the low total mass of typical globulars.Horizontal Branch morphology is potentially the largest source of uncertainty.A single-age system harbouring a large fraction of clusters with an HBmorphology systematically bluer than the one accounted for in the theoreticalcolour grid, can simulate a bimodal population with an age difference as largeas 8 Gyr. When only the redder clusters are considered, this uncertainty isalmost negligible, unless there is an extreme mass loss along the Red GiantBranch phase. The metal mixture affects mainly the redder clusters; the effectof colour fluctuations becomes negligible for the redder clusters, or when theintegrated Mv is brighter than -8.5 mag. The treatment of core convection isrelevant for ages below ~4 Gyr. The retrieved [Fe/H] distributions are overallonly mildly affected. Colour fluctuations and convective core extension havethe largest effect. When 1sigma photometric errors reach 0.10 mag, all biasesfound in our analysis are erased, and bimodal age populations with agedifferences of up to ~8 Gyr go undetected. The use of both (U-I)-(V-K) and(V-I)-(V-K) diagrams may help disclosing the presence of blue HB starsunaccounted for in the theoretical colour calibration.Comment: 20 pages, including 26 figures. A&A in pres

Colour–colour diagrams and extragalactic globular cluster ages