We study the semi-annual variation in geomagnetic activity, as detected in the geomagnetic indices am, aaH, AL, Dst and the four aσ indices derived for 6-hour MLT sectors (around noon, dawn, dusk and midnight). For each we compare the amplitude of the semi-annual variation, as a fraction of the overall mean, to that of the corresponding variation in power input to the magnetosphere, Pα, estimated from interplanetary observations. We demonstrate that the semi-annual variation is amplified in the geomagnetic data compared to that in Pα, by a factor that is different for each index. The largest amplification is for the Dst index (factor ∼ 10) and the smallest is for the aσ index for the noon MLT sector (aσ-noon, factor ≈ 1.1). By sorting the data by the prevailing polarity of the Y-component (dawn-dusk) of the Interplanetary Magnetic Field (IMF) in the Geocentric Solar Equatorial (GSEQ) reference frame, we demonstrate that the Russell-McPherron (R-M) effect, in which a small southward IMF component in GSEQ is converted into geoeffective field by Earth's dipole tilt, is a key factor for the semi-annual variations in both Pα and geomagnetic indices. However, the variability in the southward component in the IMF in the GSEQ frame causes more variability in power input to the magnetosphere Pα than does the R-M effect, by a factor of more than two. We show that for increasingly large geomagnetic disturbances, Pα delivered by events of large southward field in GSEQ (known to often be associated with coronal mass ejections) becomes the dominant driver and the R-M effect declines in importance and often acts to reduce geoeffectiveness for the most southward IMF in GSEQ: the semi-annual variation in large storms therefore suggests either preconditioning of the magnetosphere by average conditions or an additional effect at the equinoxes. We confirm that the very large R-M effect in the Dst index is because of a large effect at small and moderate activity levels and not in large storms. We discuss the implications of the observed "equinoctial"time-of-year (F)-Universal Time (UT) pattern of geomagnetic response, the waveform and phase of the semi-annual variations, the differences between the responses at the June and December solstices and the ratio of the amplitudes of the March and September equinox peaks. We also confirm that the UT variation in geomagnetic activity is a genuine global response. Later papers will analyse the origins and implications of the effects described.