So a direct comparison of the 2 numbers is probably simplistic. from the report's footnotes:
3 NB: This is a notably smaller proportion of the population identifying as Christian
than recorded by the national Censuses of both 2001 and 2011. The discrepancy
between the Census and a large number of other social surveys (which generally
concur with the BSAs lower figures) has been much discussed. While this is
not the place to delve too deeply into technical issues, it is worth noting that the
Census religion question (What is your religion?) is rather different to the BSAs
(What religion, if any, do you consider yourself belonging to?). On this subject,
see: D. Voas and S. Bruce, Research Note: The 2001 Census and Christian
Identification in Britain, Journal of Contemporary Religion 19/1 (2004), 23-8; and
A. Day, Believing in Belonging: Belief and Social Identity in the Modern World
(Oxford: Oxford University Press, 2012).
http://www.stmarys.ac.uk/benedict-xvi/docs/2016-may-contemporary-catholicism-report.pdf
Figure 1.3 in the report shows a slow increase in 'no religion' since 1983, from about 40%.