Census team brought in over unfilled forms
Officials who can conduct interviews under caution are being deployed to visit householders who failed to return the 2011 census.
Nearly 10% of 26 million households in England and Wales have yet to fill in the questionnaire, which was supposed to have been completed around 27 March.
Reminders have been sent and 29,000 collectors have visited homes to offer help with completing the questionnaire.
Anyone who refuses to take part faces prosecution and a fine of up to £1,000.
ONS census director Glen Watson said: "We are now in the final phase of follow-up and people need to act straightaway to avoid the risk of a fine.
"We realise people lead busy lives and completing their census might not be at the top of their 'to do' list, but the time to act is now.
"Where people refuse to complete their form, a formal investigation is undertaken and they can be interviewed under caution, evidence gathered and those details passed to the Crown Prosecution Service.
"The census provides vital information to enable planners to identify future local needs for housing, roads, school places, healthcare and other public services needed by local communities.
"It also gives a much clearer picture of how much society is changing over time.
"That's why we need everyone to respond and why there is a legal requirement for everyone to fill in the questionnaire.
"Our emphasis has always been to help people complete and return their form as quickly as possible.
"Prosecution is very much the last resort."