Quantum phase transitions out of a symmetry protected topological (SPT) phase in (1+1) dimensions which is gapped, into an adjacent topologically distinct phase, are typically described by a conformal field theory (CFT). We show that, very generally, the low-lying entanglement spectrum of any gapped phase in infinite space close to such a quantum critical point is universal and described by the gapless theory describing the quantum critical point (the CFT), but on a finite interval. Each gapped phase in the vicinity of the quantum critical point determines specific boundary conditions on the interval. Using this connection we show that the transformation properties of these boundary conditions under the symmetry group protecting the phase can be used to characterize the degeneracies of the entanglement spectrum, a hallmark of any non-trivial SPT phase. In particular, these boundaries are shown to carry a certain quantum anomaly which determines the topological class of the SPT phase. We also relate this discussion to the long-known 'puzzling' property of the Corner Transfer Matrix of integrable classical Stat. Mech. models with finite correlation length on a 2D lattice (Ising models and generalizations), stating that its spectrum corresponds precisely to that of the critical system (with infinite correlation length), but in finite size. - No specialized knowledge of conformal field theory or integrable systems will be assumed in the talk.