The ionosphere is one of the main factors affecting the accuracy of global navigation satellite systems (GNSS). It is a dispersive medium for radio signals, and for multi-frequency receivers, most of its effect can be removed. The problem is for the single-frequency devices, which must rely on a correction model. The motivation of this paper is the adoption of different ionospheric models in GPS/EGNOS (Global Positioning System/European Geostationary Navigation Overlay Service) positioning to mitigate the impact of geomagnetic storms. The aim of this article is to examine the accuracy of GPS/EGNOS single-frequency positioning. In all the examined solutions, GPS L1 data augmented with the EGNOS clock and ephemeris corrections were used in position calculation. The changes were only made to the ionospheric model. The examined scenarios are as follows: without any model (off), Klobuchar, NeQuick G, and EGNOS model. The analysed period is 6–12 September 2017, during which the last strong geomagnetic storm took place. In order to perform a reliable analysis, the study was conducted at three International GNSS Service (IGS) stations in different geographical latitudes, within the EGNOS APV-1 (Approach with Vertical Guidance) availability border. The obtained results prove that the EGNOS ionospheric model meets the aviation positioning accuracy criteria for the APV-1 approach during the studied geomagnetic storm. The EGNOS average horizontal positioning error of 0.75 m was on average almost two times lower than the other solutions. For vertical positioning, the EGNOS error of 0.93 m proved to be two times lower than those of the Klobuchar and NeQuick G models, while it was more than three times lower for the off solution.