For a detailed study of the space weather impact on the equatorial and low latitude F-region, the ionospheric response features are analysed during the periods of three recent and most severe magnetic storm events of the present solar cycle which occurred in October and November 2003, and November 2004. The F-layer base height (<I>h</I>'F), peak height (<I>hm</I>F2) and critical frequency (<I>fo</I>F2) data, from Trivandrum, an equatorial station and Delhi, a low latitude location, are examined during the three magnetic storm periods. The results of the analysis clearly shows that the height of the F-region (both <I>h</I>'F and <I>hm</I>F2), at the equator and low latitude, simultaneously increases by 200 to 300 km, in association with maximum negative excursion of <i>D_st</i> values around the midnight hours with a large depletion of ionization over the equator, which is followed by an ionization enhancement at low latitude during the recovery phase of the storm. At Delhi, fast variations up to 200 m/s are also observed in the F-layer vertical upward/downward velocity, calculated using Doppler shifts, associated with the maximum negative excursion of <i>D_st</i>. This shows that during magnetic disturbances, the equatorial ionization anomaly (EIA) expands to a much wider latitude than the normal fountain driven by the E/F-layer dynamo electric fields. It is also observed that during the main phase of the storm, at low latitude there is generally an enhancement of F-region ionization with an increase in <I>h</I>'F/<I>hm</I>F2 but in the equatorial region, the ionization collapses with a decrease in <I>h</I>'F/<I>hm</I>F2, especially after sunset hours. In addition, at the equator the normal pre-sunset hours' enhancement in <I>h</I>'F is considerably suppressed during storm periods. This might be due to changes in magnitude and direction of the zonal electric field affecting the upward <i><b>E</b></i>&times;<i><b>B</b></i> drift and hence the plasma distribution in the form of a decrease in electron density in the equatorial region and an increase in the low latitude region. In association with disturbance electric fields, the enhanced storm-induced equatorward meridional winds in the thermosphere can also further amplify the F-layer height rise at low latitudes during the post-midnight hours, as observed in two of the storm periods.