We numerically explore the many body localization (MBL) transition through the lens of the entanglement spectrum. While a direct transition from localization to thermalization is believed to be obtained in the thermodynamic limit (the exact details of which remain an open problem), in finite system sizes there exists an intermediate 'quantum critical' regime. Previous numerical investigations have explored the crossover from thermalization to criticality, and have used this to place a numerical lower bound on the critical disorder strength for MBL. A careful analysis of the high energy part of the entanglement spectrum (which contains universal information about the critical point) allows us to study the crossover from criticality to MBL, and we find evidence for such a crossover which could allow us to place a numerical upper bound on the critical disorder strength for MBL.