ABSTRACT We present UV photometry of the globular cluster NGC 1261 using images acquired with the Ultraviolet Imaging Telescope (UVIT) on board Astrosat. We performed point-spread function (PSF) photometry on four near-UV (NUV) and two far-UV (FUV) images and constructed UV colour–magnitude diagrams (CMDs), in combination with the Hubble Space Telescope (HST), Gaia, and ground-based optical photometry for member stars. We detected the full horizontal branch (HB) in the NUV and blue HB in the FUV and identified two extreme HB (EHB) stars. HB stars have a tight sequence in UV–optical CMDs, well fitted with isochrones generated (age 12.6 Gyr, [Fe/H] = −1.27 metallicity) using updated BaSTI-IAC models. Effective temperatures (Teff), luminosities, and radii of bright HB stars were estimated using the spectral energy distribution. As we detect the complete sample of UV-bright HB stars, the hot end of the HB distribution is found to terminate at the G-jump ($T_{\rm eff}\, ∼$ 11500 K). The two EHB stars, fitted well with single spectra, have Teff = 31000 K and a mass = 0.495 M⊙, and follow the same Teff–radius relation as the blue HB stars. We constrain the formation pathways of these EHB stars to extreme mass loss in the RGB phase (due either to rotation or enhanced helium) or a early hot-flash scenario.