Rishi Sunak will appoint an independent investigator to examine claims of alleged bullying against Dominic Raab, after the deputy prime minister requested an inquiry into two formal complaints that have been made against him. Raab, who said he will stay on as deputy PM and justice secretary while the process takes place, used a stand-in appearance at prime minister’s questions to insist he had always behaved properly towards staff, despite a growing list of accusations from officials. Sunak, who is returning from the G20 summit in Bali, will appoint an experienced external figure to conduct the inquiry, as No 10 has yet to replace Christopher Geidt as independent adviser on ministerial standards after his resignation in June. However, Downing Street said the prime minister would not be obliged to accept any findings, as he was the “ultimate arbiter” of the ministerial code, raising questions about the independence of any investigation. Raab has suggested he would stand down if the prime minister wanted him to, saying he would “respect whatever outcome” Sunak decided, although he has denied the bullying allegations and told MPs he was “confident” he had always behaved professionally. The Guardian can reveal that one of the formal complaints was from a group of mid-ranking policy officials at the Ministry of Justice. Sources said the complaint was initially made in spring this year in a letter to the permanent secretary at the MoJ, Antonia Romeo. They said the department’s top civil servant had “acted on” the complaint at the time by speaking to Raab and providing extra support for the officials. However, the complaint was revived in light of the recent allegations, reported in the Guardian, and a request by Sunak for complainants to come forward. Some Conservative MPs have questioned Sunak’s judgment in reappointing Raab and for insisting that his government will demonstrate “integrity, professionalism and accountability” at every level, in contrast to his predecessors but also meaning that any ministers who are regarded as falling short will have to be dealt with. In another development, Raab told MPs he had been subject to a separate complaint about him before entering parliament, with a settlement involving a confidentiality clause. Asked by the Labour MP Bambos Charalambous if he had “ever entered into a non-disclosure agreement connected to a complaint against him”, he told the Commons: “He is referring to an employment dispute that was settled before I entered the house. It wasn’t an NDA, but it did involve a confidentiality clause, which was standard at the time.” After days of allegations about Raab’s behaviour towards civil servants in three different government departments, he tweeted a letter to Sunak saying he had “just been notified” of two separate complaints against him, relating to his time as foreign secretary, and his first period as justice secretary, both under Boris Johnson. “I am confident that I have behaved professionally throughout,” Raab subsequently told PMQs on Wednesday. “But immediately I heard that two complaints had been made … I asked the prime minister to set up an independent investigation, and of course I will comply with it fully.” Sunak wrote back to Raab, saying an independent investigation was “the right course of action”. A Downing Street spokesperson said later that an independent outsider, backed up by a team of officials, would look into the allegations, although it remains unclear if they will also examine any further complaints that might be made. In his letter to Sunak, Raab said following news of the complaints, he was “writing to request that you commission an independent investigation into the claims as soon as possible”, adding: “I will cooperate fully and respect whatever outcome you decide.” Raab said he would remain in his posts and had “always sought to set high standards”, adding: “I have never tolerated bullying.” In the Commons, he said he would “thoroughly rebut and refute” any bullying claims and he took Sunak’s commitment towards professionalism as a “personal article of faith”. On Tuesday, Civil Service World cited a series of unnamed officials as saying that staff felt Raab was “gaslighting” them after telling a recent all-staff meeting at the Ministry of Justice that he had a zero-tolerance attitude towards bullying. The report, denied by a spokesperson, said Raab would often interrupt civil servants during briefings and criticise them. One source said: “We just didn’t trust that he wasn’t going to cut you off after half a sentence and say, ‘I don’t want to hear that, I don’t want to listen to you,’ which I would never want any of my staff being subjected to.”