This is quite hard to tell the pattern of vote switching from one party to another from the aggregate ward-level data alone because of the well known ecological inference problem, but some insights can be gleaned from the pattern of correlations in the changes in party shares.
If one party is gaining at the expense of another we would expect to see a strong negative correlation between the in the changes in the shares of the vote, as one tends to do relatively well where the other is doing relatively badly. Below are the correlation matrices for the ward level changes in the shares of the vote and changes in turnout from the BBC Key Wards data for both change since 2008 (when the incumbents were last elected) and change since last year.
Labour’s rise seems to have depended on squeezing minor parties and independents at least as much as the Liberal Democrats. Stronger UKIP performances clearly did damage the Conservatives, both relative to 2008 and last year. The strong negative correlation between the BNP and UKIP changes (-0.96 for change since 2008) suggest that UKIP was picking up most of the former BNP voters.
The final row in each matrix shows the correlations between party performances and the change in turnout. It has been suggested that part of the explanation for the poor Conservative and Liberal Democrat performances is that the supporters of these parties disproportionately stayed at home. If there was a strong tendency of this kind then we should expect to see the coalition parties performing worse where turnout fell most heavily, i.e. positive correlations between the share of the vote changes for these parties and turnout change. Instead the correlations are negative or not statistically significant. So these results suggest that Conservative and Liberal Democrat voters were not disproportionately staying at home.
Note that these are pairwise correlations so the N’s will vary, and for the ones between minor parties they can be very small. aoth refers to all others collectively. The changes are only calculated for when a party stood both times, so these matrices say nothing about the effects of candidate entry or withdrawl. Correlations that are statistically significantly different from zero at the 5% level are starred.
Thanks to the BBC, John Curtice, Rob Ford and Jon Mellon. This who provided data and analysis. The views and errors are all mine.