They would have to say that the (now) husband was the father of the child, but whether that was true or not isn't something that could, or would, be checked.....and still wouldn't today.
At that time, for a re-registration under the Legitimacy Act both parents had to have been free to marry at the time of the birth (even though they didn't) ..e.g. neither could have been married to someone else in 1927. That part of the legislation no longer applies.
If the informant lied about any of the information they gave for the re-registration then they were committing an offence of perjury for which they could be imprisoned (if discovered).