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This paper investigates the integrability properties of Einstein's theory ofgravity in the context of accelerating Newman-Unti-Tamburino (NUT) spacetimesby utilizing Ernst's description of stationary and axially symmetricelectrovacuum solutions. We employ Ehlers transformations, Lie point symmetriesof the Einstein field equations, to efficiently endorse accelerating metricswith a nontrivial NUT charge. Under this context, we begin by rederiving theknown C-metric NUT spacetime described by Chng, Mann, and Stelea in astraightforward manner, and in the new form of the solution introduced byPodolsk\'y and Vr\'atn\'y. Next, we construct for the first time anaccelerating NUT black hole dressed with a conformally coupled scalar field.These solutions belong to the general class of type I spacetimes and,therefore, cannot be obtained from any limit of the Pleban\'ski-Demia\'nskifamily whatsoever and their integration needs to be carried out independently.Including Maxwell fields is certainly permitted, however, the use of Ehlerstransformations is subtle and requires further modifications. Ehlerstransformations not only partially rotate the mass parameter such that itsmagnetic component appears, but also rotate the corresponding gauge fields.Notwithstanding, the alignment of the electromagnetic potentials can besuccessfully performed via a duality transformation, hence providing a novelReissner-Nordstr\"om-C-metric NUT black hole that correctly reproduces theReissner-Nordstr\"om-C-metric and Reissner-Nordstr\"om-NUT configurations inthe corresponding limiting cases. We describe the main geometric features ofthese solutions and discuss possible embeddings of our geometries in externalelectromagnetic and rotating backgrounds.

Ehlers transformations as a tool for constructing accelerating NUT black holes