The authors present a cell renormalisation approach for the biased self-avoiding walks and show that a stiff-to-isotropic crossover exponent is exactly one in all dimensions and for all cell sizes. They also show, by use of renormalisation flow diagrams, a substantial difference between two and three dimensions in the crossover from stiff limit to isotropic limit as the length of walk N to infinity for fixed gauche weight p. In three dimensions, a crossover seems to occur first to the random walk limit and then to the self-avoiding walk limit, while, in two dimensions, it seems to occur directly to the self-avoiding walk limit in agreement with recent observations based on Monte Carlo simulations.