Information is available on the number of dwellings rather than tenants. Local authorities in England report information for numbers of local authority owned (council) dwellings as at 1 April in their annual Housing Strategy Statistical Appendix (HSSA) returns. This information is published on the Communities and Local Government website in Table 116:
http://www.communities.gov.uk/documents/housing/xls/140882.xls
This information is not available for constituencies.