We present XMM-Newton and Chandra observations of 1E 1048.1 - 5937 , being the first to show evidence for a significant variation in the X-ray luminosity of this Anomalous X–ray Pulsar ( AXP ) . While during the first XMM-Newton ( 2000 December ) and Chandra ( 2001 July ) observations the source had a flux consistent with that measured on previous occasions ( \sim 5 \times 10 ^ { -12 } erg cm ^ { -2 } s ^ { -1 } ) , two more recent observations found it at a considerably higher flux level of 2 \times 10 ^ { -11 } erg cm ^ { -2 } s ^ { -1 } ( 2002 August ; Chandra ) and 10 ^ { -11 } erg cm ^ { -2 } s ^ { -1 } ( 2003 June ; XMM-Newton ) . All the spectra are fit by the sum of a blackbody with kT \sim 0.6 keV and a power law with photon index \sim 3 . No significant changes were seen in the spectral parameters , while the pulsed fraction in the 0.6-10 keV energy range decreased from \sim 90 % in 2000 to \sim 53 % in 2003 . The spectral invariance does not support the presence of two physically distinct components in the AXP emission . The sparse coverage of the data does not permit us to unambiguously relate the observed variations to the two bursts seen from this source in the fall of 2001 .