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The relativistic electron distribution that occupies the outer radiation belt has been observed to vary significantly during intervals of disturbed solar wind conditions. Of particular interest are the order of magnitude increases in the relativistic electron flux that sometimes, but not always, follow the onset of a magnetic storm. These currently unpredictable relativistic electron flux enhancements are potentially hazardous during space missions causing radiation damage to spacecraft instrumentation and to humans. The work presented here establishes the conditions in the solar wind that lead to such flux enhancements. In addition, through the combined analysis of electron and wave data we provide essential constraints for the numerous proposed mechanisms for the acceleration of relativistic electrons in the outer radiation belt. The study uses data from the two STRV micro-satellites, which uncommonly are in the necessary orbit to provide coverage of almost the total electron population of the outer radiation belt essential for understanding the dynamics of the electron population. Data on the > 0.75 MeV energy electrons is used to investigate the relationship between the electron flux enhancements during magnetic storms and the coincident solar wind and geomagnetic conditions. Three distinct different types of electron responses arc identified, with outcomes that are shown to strongly depend on the solar wind speed and in particular the interplanetary magnetic field orientation during the magnetic storm recovery phase. A number of the electron acceleration mechanisms proposed to explain relativistic electron flux enhancements are driven by Pc5 pulsations in the magnetosphere. We thus investigate the relationship between these waves and electron response during magnetic storms. The findings point to a strong correlation between the Pc5 energy present during flux enhancement events and the size of the subsequent flux increase. However, the strength of the Pc5 power falls off quickly in the vicinity of the peak flux enhancement. In order to separate non-adiabatic processes, such as electron loss and most importantly heating, from adiabatic effects, we represent the electron data in a canonical coordinate system of the three adiabatic invariants. M, J and &phis; during two case studies. Using this method we identify an internal source of accelerated relativistic electrons and a further source of relativistic electrons at larger L supplied via substorm injections and inward radial diffusion. We also confirm the absence of either source of relativistic electrons when the IMF is northward during the recovery phase. Finally we use the results to help validate or discredit the various proposed electron acceleration mechanisms and end by identifying the mechanism that fits most convincingly with the analysis.