Figures showing the number of families receiving child benefit (CB) at regional and parliamentary constituency level for the UK are published on the HMRC website:
http://www.hmrc.gov.uk/stats/child_benefit/geographical.htm
Figures showing the number of families eligible to claim CB are not available at these levels of geography.
Whether or not a CB recipient is currently a single parent or part of a couple is not recorded on the CB system as after 5 July 1998 it did not affect the level of award.