The child sex abuse inquiry is to write to Michael Gove to ask whether he attempted to find out about the release of an investigation into a priest suspected of abuse at a prominent Catholic boarding school.

The alleged interest of the former secretary of state for education in a police and local authority inquiry into the priest surfaced during evidence given to the Independent Inquiry into Child Sexual Abuse (IICSA) last month.

Gove, now the environment secretary, denies making any phone calls to the local authority in relation to the investigation. A search of education department telephone records, his office has said, can find no trace of any such contacts.

In a statement to the Guardian, IICSA said: “The Roman Catholic Church hearings are ongoing and there are a number of matters that require further investigation, including the evidence heard on 13 December 2017 in relation to the former secretary of state for education. The inquiry will be making requests for further information on this issue.”

The priest, only identified by the reference number F65, is alleged to have had “connections to some quite senior figures”. In evidence given to the inquiry on 13 December, F65 was said to have been the subject of an allegation of oral sex with a 16-year-old boy.

That allegation, IICSA’s inquiry into the Catholic church’s Benedictine schools heard, was investigated by the police and local authority between 2010 and 2012. It resulted in a file being sent to the Crown Prosecution Service but did not lead to any charges because there was deemed to be insufficient evidence.

F65, however, was made the subject of a “covenant of care” by the Catholic diocese of Clifton, which was intended “to manage perceived risks” when he moved to another institution.

Claire Winter, the deputy director of children’s services responsible for children’s social care at Somerset county council, gave evidence to the sex abuse inquiry about the investigation on 13 December.

Towards the end of her evidence, counsel to the inquiry, Riel Karmy-Jones QC, indicated that Winter wanted to raise a further issue. The lawyer said: “There was significant interest from the office of the secretary of state in relation to one individual, F65, a priest who had previously resided at Downside Abbey. How did that come about?”

Winter then recounted the alleged sequence of events. “I only mentioned it because it was so unusual,” she explained. “I have never experienced it before or since. This was a priest who there were concerns about and it was agreed that the abbot would suspend him from ministry while investigations continued.

“He did have, I discovered subsequently, connections to some quite senior figures, and it was one afternoon I had I think it was two phone calls from the office of the minister of state for education asking for the time at which that decision was going to be made. I said, I knew what time it was, but I said it was a child protection matter and that I wasn’t willing to discuss it.

“Then very shortly before the time it was due to happen, I had a phone call from somebody who said they were the secretary of state for education and please would I tell them the time at which – he was quite insistent about the time that decision was due to be made.

“ ... I said exactly the same thing, that it was a child protection matter, it was in relation to a criminal matter, and I couldn’t give that information ... I had no further contact after that, but it just seemed very unusual for that to happen.”

Somerset county council told the Guardian that Winter could not elaborate on her evidence.

A spokesperson for the environment secretary said: “The secretary of state does not remember any such incident and a search by the Department for Education has not found a record of any such phone call. No official or adviser that we have checked with remembers such an incident. We will of course fully cooperate with the inquiry if asked to contribute.”