We construct Tully–Fisher relationships (TFRs) in the u, g, r, i and z bands and stellar mass TFRs for a sample of 25 698 late spiral-type galaxies (with 0.045 < z < 0.085) from the Sloan Digital Sky Survey (SDSS) and study the effects of environment on the relation. We use SDSS-measured Balmer emission line widths, vFWHM, as a proxy for disc circular velocity, vcirc. A priori, it is not clear whether we can construct accurate TFRs given the small 3 arcsec diameter of the fibres used for SDSS spectroscopic measurements. However, we show by modelling the Hα emission profile as observed through a 3 arcsec aperture that for galaxies at appropriate redshifts (z > 0.045) the fibres sample enough of the disc to obtain a linear relationship between vFWHM and vcirc, allowing us to obtain a TFR and to investigate dependence on other variables. We also develop a methodology for distinguishing between astrophysical and sample bias in the fibre TFR trends. We observe the well-known steepening of the TFR in redder bands in our sample. We divide the sample of galaxies into four equal groups using projected neighbour density (Σ) quartiles and find no significant dependence on environment, extending previous work to a wider range of environments and a much larger sample. Having demonstrated that we can construct SDSS-based TFRs is very useful for future TFR studies because of the large sample size available in the SDSS.