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ABSTRACT Retrieval methods are a powerful analysis technique for modelling exoplanetary atmospheres by estimating the bulk physical and chemical properties that combine in a forward model to best fit an observed spectrum, and they are increasingly being applied to observations of directly imaged exoplanets. We have adapted taurex3, the Bayesian retrieval suite, for the analysis of near-infrared spectrophotometry from directly imaged gas giant exoplanets and brown dwarfs. We demonstrate taurex3’s applicability to sub-stellar atmospheres by presenting results for brown dwarf benchmark GJ 570D which are consistent with previous retrieval studies, whilst also exhibiting systematic biases associated with the presence of alkali lines. We also present results for the cool exoplanet 51 Eri b, the first application of a free chemistry retrieval analysis to this object, using spectroscopic observations from GPI and SPHERE. While our retrieval analysis is able to explain spectroscopic and photometric observations without employing cloud extinction, we conclude this may be a result of employing a flexible temperature-pressure profile which is able to mimic the presence of clouds. We present Bayesian evidence for an ammonia detection with a 2.7σ confidence, the first indication of ammonia in a directly imaged exoplanetary atmosphere. This is consistent with this molecule being present in brown dwarfs of a similar spectral type. We demonstrate the chemical similarities between 51 Eri b and GJ 570D in relation to their retrieved molecular abundances. Finally, we show that overall retrieval conclusions for 51 Eri b can vary when employing different spectral data and modelling components, such as temperature–pressure and cloud structures.