Eclipsing binary systems provide the opportunity to measure fundamental parameters of their component stars in a stellar-model independent way. This makes them ideal candidates for testing and calibrating theories of stellar structure and (tidal) evolution. Large photometric (space) surveys provide a wealth of data for both the discovery and the analysis of these systems. Even without spectroscopic follow up there is often enough information in their photometric time series to warrant analysis, certainly if there is an added value present in the form of intrinsic variability like pulsations. Our goal is to implement and validate a framework for the homogeneous analysis of large numbers of eclipsing binary light curves such as the numerous high duty-cycle observations from space missions like TESS. The aim of this framework is to be quick and simple to run and to limit the user's time investment in obtaining, amongst other parameters, orbital eccentricities. We develop a new and fully automated methodology for the analysis of eclipsing binary light curves with or without additional intrinsic variability. Our method includes a fast iterative prewhitening procedure resulting in a list of extracted sinusoids that is broadly applicable for purposes other than eclipses. After eclipses are identified and measured, orbital and stellar parameters are measured under the assumption of spherical stars of uniform brightness. We test our methodology in two settings: a set of synthetic light curves with known input and the catalogue of Kepler eclipsing binaries. The synthetic tests show that we can reliably recover the frequencies and amplitudes of the sinusoids included in the signal as well as the input binary parameters, albeit to varying degrees of accuracy. Recovery of the tangential component of eccentricity is most accurate and precise. Kepler results confirm a robust determination of orbital periods, with 81.8% of periods matching the catalogued ones. We present the eccentricities for this analysis and show that they broadly follow the theoretically expected pattern as a function of the orbital period. Our analysis methodology is shown to be capable of analysing large numbers of eclipsing binary light curves with no user intervention, and provide in that a basis for the further in-depth analysis of systems of particular interest as well as for statistical analysis at the sample level. Furthermore the computational performance of the frequency analysis, extracting hundreds of sinusoids from Kepler light curves in a few hours, demonstrates its value as a tool for a field like asteroseismology.