Bluewave Geographics have released their demographic data pack from the 2021 census for England & Wales
The data pack is available at a number of geographical levels, including
Census output areas
LSOAs
Local/unitary authorities
Parliamentary constituencies
Postcode sector, district and area
and includes the following topics:
Population and Households
Age/sex
Working status by sex
Full-time/Part-time working by sex
Housing Tenure (Households)
Accommodation Type
Ethnicity
Country of birth
Religion
Occupation (current)
Industry
Marital and civil partnership status
Disability
Qualifications
Persons per household
Rooms per household
Bedrooms per household
Occupancy rate: bedrooms
Occupancy rate: rooms
Households with cars or vans
Household composition
Distance travelled to work
Method of travel to work
NS-Sec
Household deprivation
You can see the the the full definition of the pack   here