When closing or merging a Jobcentre, the Department for Work and Pensions (DWP) undertake an equality analysis as part of the detailed planning for service reconfiguration. This will include feedback from public consultation in those locations where this applied. Details of jobcentres that have closed and/or merged in the last two years can be found at: https://www.gov.uk/government/news/update-on-the-future-of-dwp-jobcentres
The Ministry of Housing, Communities and Local Government publishes local authority data on homelessness applications quarterly.
Reference should also be made to the response given on 9 February 2018 in the reply to PQ 126480.