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We present new accurate CCD uvby light curves for the LMC eclipsing binaries HV 982 and HV 12578, and for the SMC systems HV 1433 and HV 11284 obtained at the Danish 1.5m telescope at ESO, La Silla. The light curves were derived from DoPHOT photometry, and typical accuracies are between 0.007 and 0.012mag per point. Standard uvby indices have also been established for each binary, primarily for determination of interstellar reddening and absorption. For HV 982 and HV 12578, accurate photometric elements have been established. Both systems consist of two detached components of comparable sizes in an eccentric orbit. Adopting the spectroscopic elements given by Fitzpatrick et al. (2002ApJ...564..260F) for HV 982, we derive absolute dimensions of its components which agree well with their results. A distance modulus of V₀-M_V=18.63±0.08 is obtained, corresponding to a distance of 53.2±2.0kpc, which is in formal agreement with (although slightly larger than) their determination. HV 1433 and HV 11284 both consist of two rather close, deformed and quite different stars. As the mass ratios between the components (and their rotation rates) are not known, definitive photometric elements can not yet be obtained, but we present a sample of possible photometric solutions. In a series of forthcoming papers we will combine our uvby observations with high-dispersion spectra from the UVES spectrograph on the ESO Very Large Telescope (VLT) and present absolute dimensions, chemical abundances and distances for selected LMC and SMC systems, including HV 12578 and refined results for HV 982.