I have seen census data about the father whereabouts after the first marriage and the birth of the child. This shows two closed records at the address.
Does anyone know why records are 'closed' and why the information is witheld?
Do you mean the 1939 register? This is not a census. It was continually updated by the NHS. The redacted (blocked out entries) are people who were born less than 100 years ago who were not known to have died. (Although there are some exceptions). Because they may still be living. They get unblocked as the years go by, so by 2039 the whole thing should be visible.
Reasons for not known to have died are, that they haven’t died, or they may have died in another country, thus not showing on English data bases.