LONDON — The British police said on Saturday that a leak that led Prime Minister Theresa May to abruptly fire her defense secretary, Gavin Williamson, this past week did not constitute a crime and they would not investigate the matter.

“No crime has been committed and this is not a matter for the police,” Assistant Commissioner Neil Basu, head of special operations at the Metropolitan Police, said in a statement, after calls from Mr. Williamson and some lawmakers for an investigation.

“I am satisfied that the disclosure did not amount to a criminal offense, either under the Official Secrets Act or Misconduct in a Public Office,” Mr. Basu wrote in the statement.

Mr. Williamson has denied leaking discussions from Britain’s National Security Council and had called for a police investigation to clear his name. Having led Mrs. May’s campaign to become the leader of the Conservative Party, he was reported to have had leadership ambitions of his own.