The Health Data Finder for Research mainly covers the health data sets only. The Data Custodians, though, have access to other non-health data sets, such as
Birth and mortality data from ONS
Indices of deprivation from the Department for Communities and Local Government
Statistics on education and children from the Department for Education
If you are interested in an existing data sets, regardless whether within health or not, we recommend you to discuss your requirement with the data custodian experts.