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We present H I-based B- and R-band Tully-Fisher relations (TFRs) and the Baryonic TFR (BTFR) at z = 0.2 using direct H I detections from the Blind Ultra-Deep H I Environmental Survey (BUDH IES). Deep photometry from the Isaac Newton Telescope was used for 36 out of 166 H I sources, matching the quality criteria required for a robust TFR analysis. Two velocity definitions at 20 and 50 per cent of the peak flux were measured from the global H I profiles and adopted as proxies for the circular velocities. We compare our results with an identically constructed z= 0 TFR from the Ursa Major association (UMa) of galaxies. To ensure an unbiased comparison of the TFR, all the samples were treated identically regarding sample selection and applied corrections. We provide catalogues and an atlas showcasing the properties of the galaxies. Our analysis is focused on the zero points of the TFR and BTFR with their slopes fixed to the z = 0 relation. Our main results are: (1) The BUDH IES galaxies show more asymmetric H I profiles with shallower wings compared to the UMa galaxies, which is likely due to the environment in which they reside, (2) The luminosity-based z= 0.2 TFRs are brighter and bluer than the z = 0 TFRs, even when cluster galaxies are excluded from the BUDH IES sample, (3) The BTFR shows no evolution in its zero point over the past 2.5 billion yr and does not significantly change on the inclusion of cluster galaxies, and (4) proper sample selection and consistent corrections are crucial for an unbiased analysis of the evolution of the TFR.