Referee 1's Review (Dr. Andy Tatem):

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N.B. These are the comments made by the referee when reviewing an earlier version of this paper. Prior to publication the manuscript has been revised in light of these comments and to address other editorial requirements.
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This paper represents an excellent example of the application of theoretical models to real world situations, underlining the importance of taking into account the spatial details of the region examined and properly parameterizing models with data. I have no hesitation in recommending it for publication. A few minor points are as follows:

1. It would be nice to see a bit more discussion of the potential implications/applications of the findings to e.g. modern day Britain, other parts of the world or other diseases. Just a single paragraph would suffice on this to help readers see how the results are significant not only for measles in Britain 50 years ago. Also, how do things change in todays modern world where there is far more movement than 50 years ago?
2. Unless I have misread things, it is unclear when the CCS threshold was applied - ie in the time between 1944 and 1964, I imagine a few cities crossed the 300,000 threshold to become core cities - were these changes incorporated? How would things vary today/elsewhere in the World where there are many many more cities of >300,000?
3.Although it may not make too much of a significant difference for the short distances in the UK, distances between latitude and longitude pairs should be calculated using geodesic curve great circle distances, not Euclidean - this could be important in applying such models elsewhere.