  We study the vortex-line lattice and liquid phases of a clean type-II
superconductor by means of Monte Carlo simulations of the lattice London model.
Motivated by a recent controversy regarding the presence, within this model, of
a vortex-liquid regime with longitudinal superconducting coherence over long
length scales, we directly compare two different ways to calculate the
longitudinal coherence. For an isotropic superconductor, we interpret our
results in terms of a temperature regime within the liquid phase in which
longitudinal superconducting coherence extends over length scales larger than
the system thickness studied. We note that this regime disappears in the
moderately anisotropic case due to a proliferation, close to the flux-line
lattice melting temperature, of vortex loops between the layers.
