We report the observation of an unusual field direction dependent second magnetisation peak (SMP) anomaly at very low fields, close to the field of full penetration Hp, in an aluminium-doped single crystal of YBa2Cu3−xAlxOδ, for H c. Such an anomaly is observed at different field values in the field ramp-up direction (H) compared to the field-down direction (H), and it is also found to persist to different temperatures. For the field-up direction, it is observed in the range of 8 K to 30 K (upper range extendible to 40 K depending on the crystal), while for the field-down direction, it is observed between 8 K to 65 K (upper range extendible to 70 K depending on the crystal). The temperature dependence of the fields of full penetration Hp, the onset field of the SMP anomaly, as well as the central magnetisation peak, seem to be affected by surface barriers at low temperatures, where they are seen to rise anomalously. An exponential fit to the low temperature penetration field and central magnetisation peak width, as well as an asymmetric magnetisation towards the irreversibility field, illustrate the effect of surface barriers at low temperatures. At higher temperatures, the onset field of the SMP anomaly is described well by a dislocation mediated order–disorder transition. The temperature dependence of the peak field of the second magnetisation anomaly, however, does not seem to be affected by the surface barrier and is well described by a power law. An oxygen deficient aluminium cluster model is used to explain the differences in the SMP anomalies in the two quadrants. Two vortex phase diagrams, one for each field direction, have been made describing the various phases.