Microtubule arrays effect cell polarisation by directing cellular cues for cortical remodelling and growth. Their function depends crucially on the intrinsic dynamic properties of constituent microtubules. Microtubule dynamicity is restricted to a certain range within the confines of a cellular geometry. Thus it is of great interest to determine whether rescaling of dynamic properties of microtubules has consequences for cell polarity. We constructed fission yeast strains exhibiting depressed microtubule dynamics by mutating the β-tubulin gene, nda3. This interfered with efficient accumulation of a polarity factor Tea1 at cell tips. Interestingly, the polarity machinery in the mutant cells was highly susceptible to perturbations. Simulations of growth zone formation followed by imaging of actin distribution showed a significantly delayed onset of bipolar growth. We propose that there exists a threshold of microtubule dynamicity that allows robust cellular polarisation.