Using small angle neutron scattering we have studied the square to hexagonal flux line lattice symmetry transition in different members of the borocarbide superconductors. The studies were performed using samples of ErNi2B2C, Lu(Ni1-xCox)(2)B2C with cobalt doping levels x = 1.5-9% and Y0.64Lu0.36Ni2B2C. We find that the onset field of the symmetry transition can be shifted more than an order of magnitude due to changes in the range of the non-local electrodynamics. Comparing the results to transport measurements of the electronic mean free path and the superconducting coherence length we find that the transition onset follows a model by V. Kogan et nl., which includes non-local corrections to the London model due to the Fermi surface anisotropy of the borocarbides. (C) 2000 Elsevier Science B.V. All rights reserved.