We report on optical integral field spectroscopy of two unrelated blue compact galaxies mapped with the 13 x 13 arcsec^2 VIMOS integral field unit at a resolution of 0.33 x 0.33 arcsec^2. Continuum and background subtracted emission line maps in the light of [O III] 5007, H-alpha, and [N II] 6584 are presented. Both galaxies display signs of ongoing perturbation and/or interaction. UM 420 is resolved for the first time to be a merging system composed of two starbursting components with an 'arm-like' structure associated with the largest component. UM 462 which is a disrupted system of irregular morphology is resolved into at least four starbursting regions. Maps of the H-alpha radial velocity and FWHM are discussed. No underlying broad line region was detected from either galaxy as the emission lines are well-fitted with single Gaussian profiles only. Electron temperatures and densities as well as the abundances of helium, oxygen, nitrogen, and sulphur were computed from spectra integrated over the whole galaxies and for each area of recent star formation. Maps of the O/H ratio are presented: these galaxies show oxygen abundances that are ~20 per cent solar. No evidence of substantial abundance variations across the galaxies that would point to significant nitrogen or oxygen self-enrichment is found (<0.2 dex limit). Contrary to previous observations, this analysis does not support the classification of these BCGs as Wolf-Rayet galaxies as the characteristic broad emission line features have not been detected in our spectra. Baldwin-Phillips-Terlevich emission line ratio diagrams which were constructed on a pixel by pixel basis indicate that the optical spectra of these systems are predominantly excited by stellar photoionization. Comment: 19 pages, 14 figures