We have used medium resolution spectra to search for evidence that proto-stellar objects accrete at high rates during their early ‘ assembly phase ’ . Models predict that depleted lithium and reduced luminosity in T-Tauri stars are key signatures of ‘ cold ’ high-rate accretion occurring early in a star ’ s evolution . We found no evidence in 168 stars in NGC 2264 and the Orion Nebula Cluster for strong lithium depletion through analysis of veiling corrected 6708 Å lithium spectral line strengths . This suggests that ‘ cold ’ accretion at high rates ( \dot { M } \geq 5 \times 10 ^ { -4 } M _ { \odot } yr ^ { -1 } ) occurs in the assembly phase of fewer than 0.5 per cent of 0.3 \leq M _ { \star } \leq 1.9 M _ { \odot } stars . We also find that the dispersion in the strength of the 6708 Å lithium line might imply an age spread that is similar in magnitude to the apparent age spread implied by the luminosity dispersion seen in colour magnitude diagrams . Evidence for weak lithium depletion ( < 10 per cent in equivalent width ) that is correlated with luminosity is also apparent , but we are unable to determine whether age spreads or accretion at rates less than 5 \times 10 ^ { -4 } M _ { \odot } yr ^ { -1 } are responsible .