We report on tunnelling magnetoresistance (TMR), current–voltage (IV) characteristics and low-frequency noise in epitaxially grown Fe(110)/MgO(111)/Fe(110) magnetic tunnel junctions (MTJs) with dimensions from 2×2 to 20×20μm 2 . The evaluated MgO energy barrier (0.50±0.08eV), the barrier width (13.1±0.5Å) as well as the resistance times area product (7±1MΩμm 2 ) show relatively small variation, confirming a high quality epitaxy and uniformity of all MTJs studied. At low temperatures (T<10K) inelastic electron tunneling spectroscopy (IETS) shows anomalies related to phonons (symmetric structures below 100meV) and asymmetric features above 200meV. We explain the asymmetric features in IETS as due to generation of electron standing waves in one of the Fe electrodes. The noise power, though exhibiting a large variation, was observed to be roughly anti-correlated with the TMR. Surprisingly, for the largest junctions we observed a strong enhancement of the normalized low-frequency noise in the antiparallel magnetic configuration. This behavior could be related to the influence of magnetostriction on the characteristics of the insulating barrier through changes in local barrier defects structure.