  We carry out Monte Carlo simulations of the three dimensional (3D) lattice
London superconductor in zero applied magnetic field, making a detailed finite
size scaling analysis of the Meissner transition. We find that the magnetic
penetration length \lambda, and the correlation length \xi, scale as \lambda ~
\xi ~ |t|^{-\nu}, with \nu = 0.66 \pm 0.03, consistent with ordinary 3D XY
universality, \nu_XY ~ 2/3. Our results confirm the anomalous scaling dimension
of magnetic field correlations at T_c.
