Gavin Williamson undermined for a period the trust of intelligence agencies and others that was needed for them to offer unvarnished advice to ministers when he allegedly leaked information from the national security council (NSC) as defence secretary, Theresa May has said. Giving evidence to a parliamentary committee, the former prime minister also hit out again at Boris Johnson’s decision to appoint his chief Brexit negotiator, David Frost, as national security adviser, saying she was glad this eventually did not happen. May described events in May 2019, when she sacked Williamson from the cabinet after an investigation concluded he had leaked discussions about the role of Chinese telecoms firm Huawei in the UK’s 5G network, as a “shock to the system”. Williamson, who claimed he was the victim of a “kangaroo court”, was swiftly returned to ministerial office, as education secretary, after Johnson succeeded May. Questioned by the national security strategy committee, which includes both peers and MPs, May was asked by its chair, Labour’s Margaret Beckett, about the damage done to the workings of the NSC by Williamson’s actions. “Obviously, an incident like that is a shock to the system when it happens, and I think there was a slight sense, initially, of concern, particularly, obviously, those who weren’t the politicians sitting around the table, about the advice and evidence that they were giving in to the council,” she said. “Because it had always been the case that the assumption was – and it had, practically, been the case since it was set up – that nothing leaked from the national security council. And it’s really important that nothing leaks from it, because of the nature of the discussions we’re having. “And you want the agencies, Ministry of Defence and others who are advising you to believe and feel confident that they have the freedom to give their best and genuine advice, without feeling that they’ve got to hold something back.” There was, May said, “a slight judder, if you like, when this incident happened, when people were concerned initially”, adding: “But I think we then got back into the rhythm of people recognising that they could speak as freely as they had done previously.” May had previously criticised Johnson’s announcement last June that Frost was to become national security adviser, asking why the job had gone to someone “with no proven expertise in national security”. In January, Johnson changed his mind, making Frost, now a peer, his ministerial lead on Brexit, and appointing Sir Stephen Lovegrove, the permanent secretary of the Ministry of Defence, as national security adviser. May raised the issue tangentially herself, when discussing her decision as prime minister to have the national security adviser role combined with being cabinet secretary under Mark Sedwill. “Dare I say it, I think it’s more important to have a national security adviser who has some security experience, albeit also as cabinet secretary, than one who doesn’t have any security experience,” she said. Asked by the crossbench peer Herbert Laming about her thoughts on Frost being lined up for the job, May said prior experience and expertise was vital. “The national security adviser is the person the prime minister and the government look to, to give absolutely critical, independent, well-analysed views on the security situation, be it if you’re discussing a relationship with another country, or an internal domestic security issue,” she said. “I think it’s therefore important that that individual has experience in the security field.” May added: “I think it is so important to have security experience, and to have been in that world, to understand it, and to be able to slot in, immediately, in dealing with those issues. “And that was my concern about the appointment of David Frost. That was now changed.” Lovegrove was, May said, “steeped” in security issues, and “will do a very good job”.