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Results are reported of Monte Carlo renormalisation group studies of the approach to asymptotic scaling in SU(3) lattice gauge theory. By comparing measurements on 8 4 and 16 4 lattices, estimates are obtained for the shift, [Delta][beta], in the fundamental plaquette coupling, [beta9, corresponding to a change of length scale by a factor of 2. The definitions of block link variables contain a free parameter whose value can be optimised to minimise the transient flow to a renormalised trajectory. Our results, at [beta] = 6.0, 6.3 and 6.6, are consistent with those obtained previously with the improved ratio method, which is also briefly discussed. In both methods simulation is performed only with the standard Wilson action. An important feature of the results is the appearance of a pronounced dip in [Delta][beta] which implies that in the presently accesible range of [beta] the asymptotic value is approached from below, and its onset is delayed.