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Your GPX is most certainly in WGS84. Set the project CRS to EPSG 193627700, the GPX to 4326 and the raster to 193627700 and enable on-the-fly reprojection.
Your GPX is most certainly in WGS84. Set the project CRS to EPSG 1936, the GPX to 4326 and the raster to 1936 and enable on-the-fly reprojection.
Your GPX is most certainly in WGS84. Set the project CRS to EPSG 27700, the GPX to 4326 and the raster to 27700 and enable on-the-fly reprojection.