No, the Government already has this information. Everything is recorded and collated by the respective government departments, including all the data held by local councils. How do you think the ONS produces its regular reports?
As for estimating what new school places might be required, that can be estimated from birth records, local voting rolls/council tax registers and current nursery attendance. And of course the census is only done every 10 years, which would be no use for this purpose anyway.
So for example DWP and Inland Revenue have detailed records of all those working, retired, and in receipt of benefits. DES has detailed records of nursery, school and college populations. DHSC has detailed records of everyone registered with a GP and/or accessing NHS services. DVLA has detailed records of all drivers, and all vehicles on the road. And so on. And add to this all the information held by local councils.
In other words, local and central Government already has comprehensive data on pretty much every aspect of our lives, and plentiful information for planning services and infrastructure.
That's why I'm suggesting the census is now unnecessary and irrelevant, except possibly for future historians.