You asked

To give some context to my question, ONS data here, shows that around 21000 Commonwealth citizens arrived in the UK prior to 1971 and claim to not hold a passport.  

I would like to know how many - if any - times the ONS has been requested by an individual or an organisation to provide access to a census return prior to 1971 in order for them to use it as proof of residency in the UK at a certain point in time? An example would be a person of Jamaican origin who filled the 1971 census asking to use their form as proof that they were in the UK prior to 1973.

We said

​Thank you for your Freedom of Information enquiry about how many times an individual or organisation has asked ONS to provide access to a census form in order to use it as proof of residency in the UK at a certain point in time.

We can confirm that we do not hold the information you require.

In line with government policy, relevant legislation and the promise of confidentiality, personal census information is not released until 100 years after the census in question. This helps to protect personal information about people still living, whose information was recorded on these historic censuses. Therefore, currently any request to access personal information from the 1921 and subsequent censuses would be refused. Although anonymised aggregated statistics are made publicly available such as the commissioned table you refer to.