We experimentally investigate the spontaneous emission (SE) rates of single InAs quantum dots embedded in GaAs photonic nanowires. For a diameter leading to the optimal confinement of the fundamental guided mode HE11, the coupling to HE11 dominates the SE process and an increase of the SE rate by a factor of 1.5 is achieved. When the diameter is decreased, the coupling to this mode vanishes rapidly, thus allowing the coupling to the other radiation modes to be probed. In these conditions, a SE inhibition factor of 16, equivalent to the one obtained in state-of-the-art photonic crystals, is measured. These results, which are supported by fully vectorial calculations, confirm the potential of photonic nanowires for a nearly perfect, broadband SE control.