According to https://www.ons.gov.uk/census
The Office for National Statistics (ONS) is responsible for planning and carrying out the census for England and Wales. The next census will take place on 21 March 2021.
When will results be published?
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Provisional release date: March to April 2022. The initial findings from the 2021 Census of Population and Housing in England and Wales, that took place on 21 March 2021. Statistics from the 2021 Census will be released in stages over the next year.