We report on simultaneous radio and X-ray observations of the radio-emitting magnetar 1E1547.0-5408 on 2009 January 25 and February 3, with the 64-m Parkes radio telescope and the Chandra and XMM-Newton X-ray observatories. The magnetar was observed in a period of intense X-ray bursting activity and enhanced X-ray emission. We report here on the detection of two radio bursts from 1E1547.0-5408, reminiscent of Fast Radio Bursts (FRBs). One of the radio bursts was anticipated by ~1s (about half a rotation period of the pulsar) by a bright SGR-like X-ray burst, resulting in a F_radio/F_X ~ 10^-9. Radio pulsations were not detected during the observation showing the FRB-like radio bursts, while they were detected in the previous radio observation. We also found that the two radio bursts are neither aligned with the latter radio pulsations nor with the peak of the X-ray pulse profile (phase shift of ~0.2). Comparing the luminosity of these FRB-like bursts and those reported from SGR1935+2154, we find that the wide range in radio efficiency and/or luminosity of magnetar bursts in the Galaxy may bridge the gap between ordinary pulsar radio bursts and the extragalactic FRB phenomenon.