The acceleration of ions (∼108 cm/s) has been observed in the laser produced plasma expanding across an uniform magnetic field at low laser irradiance (∼5 × 1012 W/cm2). This acceleration was found correlated with the onset of instabilities in the plasma and decrease in the slope of X-ray emission with laser intensity. A large enhancement in the X-ray emission (E > 2 KeV) from plasma in the presence of magnetic field supports the observation of ion acceleration. An increase in the number of ions was noticed in the pressure range in which enhancement in the self-generated spontaneous magnetic field has already been established. Even scaling of both the variations with chamber pressure during rising part was found in close agreement, which further supports the correlation. The possibility of an external magnetic field in triggering the acceleration and space charge potential in generating a correlation (between ion acceleration and self-generated spontaneous magnetic field) has been discussed.