ESO 338-IG04 , also known as Tololo 1924-416 , is a well known luminous blue compact galaxy in the local universe . Images obtained with the Hubble Space Telescope ( HST ) have shown that the central starburst region is composed of numerous bright point sources - young star clusters , surrounded by a population of old and intermediate age globular clusters . In this paper we use ultra-violet ( UV ) and optical HST photometry in five bands , and an extensive set of spectral evolutionary synthesis scenarios to investigate the age and masses of 124 star clusters . The very small reddening makes ESO 338-IG04 an excellent laboratory for studying the formation of such objects . We find that a careful treatment of the nebular emission component is crucial when modelling the broad-band colours of young starburst regions . We have used the star clusters to trace the temporal and spatial evolution of the starburst , and to put constraints on the star formation activity over a cosmological time-scale . The present starburst has been active for about 40 Myr and shows evidence for propagating star formation and structures triggered by galactic winds . A standard Salpeter initial mass function ( IMF ) extending up to 120 M _ { \odot } provides the best fit to the data , although a flatter IMF can not be excluded . The compact star clusters provide 30-40 % of the UV luminosity and star formation activity . We find no evidence for dust obscuration even among the youngest ( < 1 Myr ) clusters , and we propose that this may be related to a short time-scale for destruction of dusty molecular clouds . Over a longer time-scale , we find evidence for previous cluster formation epochs - notably one a couple of Gyr ago . The fraction of the galaxy ’ s stellar mass contained in compact star clusters is found to be several percent , which is an unusually high value . The intermediate age clusters show a flattened space distribution which agrees with the isophotal shape of the galaxy , whereas the oldest clusters seem to have a spherical distribution indicating that they formed prior to the rest of the galaxy .