One of the perceived obstacles to electoral reform is the work and time to redraw constituency boundaries.
For AMS or AV+, redrawing the boundaries would indeed be a major task. It would also be a controversial one as, although less significant to the overall result than in First Past The Post elections, they could have some effect and every party would do its best to influence the boundaries to its own advantage.
By contrast redrawing for STV would be very simple.
The simplest way, to introduce STV quickly, would be just to amalgamate groups of about five single-member constituencies together to form multi-member constituencies, each of which would elect about five MPs by STV. During the subsequent Parliament, boundaries could be redrawn to link more with natural communities.
Better still with a little more work, the new multi-member constituencies could be based on local authority districts to provide not only a high level of proportionality, but also links with natural communities. Here is such a plan that someone prepared earlier: http://www.macs.hw.ac.uk/~denis/stv4uk.
Of course, one of STV’s many advantages is that, once drawn, constituency boundaries would rarely need changing. This would not only save work and public money but would also avoid controversy and potential gerrymandering. Moreover, it would introduce greater stability and encourage longer relationships between MPs and constituents.
If a multi–member constituency covered a town and its surrounding countryside and there was a population movement between the town and countryside but no change in the overall population, the constituency could remain unchanged.
A population change, which might be quite significant to a single-member constituency, would be less significant to a multi-member one.
When there is significant change to the population of a multi-member constituency, it may be more appropriate to change the number of MPs than to change the boundaries. This would avoid the knock-on effect on other constituencies that changing boundaries has.