We present GALEX far-ultraviolet (FUV, λeff= 1538Å) and near-ultraviolet (NUV, λeff= 2316Å) surface photometry of 40 early-type galaxies (ETGs) selected from a wider sample of 65 nearby ETGs showing emission lines in their optical spectra. We derive FUV and NUV surface brightness profiles, (FUV−NUV) colour profiles and D25 integrated magnitudes. We extend the photometric study to the optical r band from SDSS imaging for 14 of these ETGs. In general, the (FUV−NUV) radial colour profiles become redder with galactocentric distance in both rejuvenated (≤4 Gyr) and old ETGs. Colour profiles of NGC 1533, NGC 2962, NGC 2974, NGC 3489 and IC 5063 show rings and/or arm-like structures, bluer than the body of the galaxy, suggesting the presence of recent star formation. Although seven of our ETGs show shell systems in their optical image, only NGC 7135 displays shells in the UV bands. We characterize the UV and optical surface brightness profiles, along the major axis, using a Sersic law. The Sersic law exponent, n, varies from 1 to 16 in the UV bands. S0 galaxies tend to have lower values of n (≤5). The Sersic law exponent n= 4 seems to be a watershed: ETGs with n > 4 tend to have [α/Fe] greater than 0.15, implying a short star-formation time-scale. We find a significant correlation between the FUV−NUV colour and central velocity dispersions σ, with the UV colours getting bluer at larger σ. This trend is likely driven by a combined effect of ‘downsizing’ and of the mass–metallicity relation.