The paper presents studies of Bose-Einstein Correlations (BEC) for pairs of like-sign charged particles measured in the kinematic range [Formula: see text] 100 MeV and [Formula: see text] 2.5 in proton collisions at centre-of-mass energies of 0.9 and 7 TeV with the ATLAS detector at the CERN Large Hadron Collider. The integrated luminosities are approximately 7 [Formula: see text]b[Formula: see text], 190 [Formula: see text]b[Formula: see text] and 12.4 nb[Formula: see text] for 0.9 TeV, 7 TeV minimum-bias and 7 TeV high-multiplicity data samples, respectively. The multiplicity dependence of the BEC parameters characterizing the correlation strength and the correlation source size are investigated for charged-particle multiplicities of up to 240. A saturation effect in the multiplicity dependence of the correlation source size parameter is observed using the high-multiplicity 7 TeV data sample. The dependence of the BEC parameters on the average transverse momentum of the particle pair is also investigated.