Documents that refer to Mr Straubenzee, who died in 1999, had been earmarked for destruction but National Archives officials flagged them up to the Government.
The Second Church Estates Commissioner provides an important link between Government and the established Church.
Sir William van Straubenzee MP served as a member of the House of Laity from 1965 to 1970 and was elected to the General Synod in 1975, serving until 1985.
He chaired the Synod's Dioceses Commission from 1978 to 1986 and was appointed to be the Second Church Estates Commissioner in 1979, a post he held until he 1987.
A group of papers that name Mr Straubenzee, who has been described as a 'keen churchgoer' along with former Home Secretary Leon Brittan, Peter Morrison, who was an aide to Margaret Thatcher and ex-diplomat Sir Peter Hayman contain references to the Kincora children's home in Northern Ireland where boys were abused, were "found in a separate Cabinet Office store of assorted and unstructured papers".
One of the files relating to Hayman was held by the Cabinet Office but "overlooked" during a previous trawl for information.
The admission came after MPs left Westminster for the summer recess.
In a document published on the Government's website, the Home Office said a fresh search of the archives had been carried out after a file emerged earlier this year that should have been submitted to the Wanless and Whittam inquiry into the handling of allegations that prominent figures were child abusers.
Peter Wanless, head of the NSPCC, and Richard Whittam QC, reported last year that they had found no evidence that records were deliberately removed or destroyed.
After examining the latest batch of documents, they said they "found nothing to cause us to alter the conclusions drawn or recommendations made in our review".
But they warned that the emergence of papers after the review had been completed was not "helpful" in giving the public confidence in the process.
The investigators also revealed that allegations about an MP with a "penchant for small boys" were dismissed on the basis of his word with the potential political fallout the top priority rather than the risk to children.
Their report said: "There were a number of references across the papers we saw that reinforced the observation we made in our review that issues of crimes against children, particularly the rights of the complainant, were given considerably less serious consideration than would be expected today.
"To give one striking example, in response to claims from two sources that a named Member of Parliament ''has a penchant for small boys" matters conclude with acceptance of his word that he does not and the observation that 'at the present stage ... the risks of political embarrassment to the Government is rather greater than the security danger'. The risk to children is not considered at all."
Mr Wanless and Mr Whittam said the latest discovery, which came to light earlier this year, showed the need for a broader search of documents "unconstrained by what the Home Office in particular might or might not have known".
New Zealand High Court judge Lowell Goddard, who is heading up an overarching inquiry into historical child sex abuse, is set to start again from scratch.
An NSPCC spokesman said: "This is a clear illustration, as the original review revealed, of the misplaced priorities of those operating at highest levels of government, where people simply weren't thinking about crimes against children and the consequences of those crimes in the way that we would expect them to. It reiterates the need for an inquiry that will explore this in depth."
