Speaking at Prime Minister’s Questions, where she was standing in for Rishi Sunak, who is at the G20 in Bali, Mr Raab said she was “confident I conducted myself professionally throughout”. The deputy prime minister and justice secretary earlier wrote to Rishi Sunak calling for an independent inquiry into two allegations, one relating to his time as foreign secretary and the other while he was justice secretary under Boris Johnson. “I look forward to dealing with these allegations and continuing to serve as Deputy Prime Minister, Justice Secretary and Lord Chancellor,” he tweeted. Mr Sunak agreed to an investigation and his spokesman said the prime minister “still has full confidence” in his deputy. Raab takes on Rayner at PMQs – live policy updates Last week, Mr Raab faced allegations of bullying in the media, including throwing tomatoes at staff, being rude to staff and being warned for his behaviour. Asked several times about the allegations during PMQs, Mr Raab said: “I’m sure I conducted myself professionally throughout. “But immediately I heard that two complaints were made – I think they were made yesterday, I was notified this morning – I immediately asked the prime minister to do an independent investigation. And of course I will fully comply with the investigation. “ He added: “It is important that we have zero tolerance for any bullying.” Asked if he threw a tomato at a member of staff, Mr Raab said: “That never happened.” Image: Dominic Raab denied ever bullying anyone Mr Raab was asked by Labor MP Babo Haralambous whether he had “ever entered into a non-disclosure agreement relating to a complaint against him”. The deputy speaker said: “It refers to a labor dispute before I entered Parliament. “It wasn’t an NDA, but it did include a confidentiality clause, which was standard at the time.” In his letter to Mr Sunak, the deputy prime minister said he had “just been informed that two separate complaints have been formally lodged against me”. He did not say what the complaints were about or who made them. But he called for an investigation into the allegations “as soon as possible” and said he would “cooperate fully and respect whatever outcome you decide”. He added: “I have always sought to set high standards and build teams that can deliver for the British people amid the acute challenges we have faced in recent years. “I have never tolerated bullying and have always tried to strengthen and empower the groups of civil servants working in my respective departments.” Read more: The allegations against Dominic Raab Use Chrome browser for more accessible video player 8:14 Bullying claims ‘open secret’ Mr Sunak responded to his deputy’s letter and said he agreed to look into the allegations against him. “Integrity, professionalism and accountability are core values of this government. It is right that these matters are fully investigated,” he said. It is not known who will lead the inquiry into Mr Raab, as there is currently no ethics adviser following Lord Geidt’s resignation in June. Mr Sunak’s official spokesman said yesterday that the prime minister was “committed” to installing a replacement and “the process is underway to appoint a new adviser”. The president of the FDA civil servants union, Dave Penman, told Sky News on Tuesday that there had been complaints against several other current ministers, but staff were not making formal complaints as the system did not support them. Labour’s Lisa Nundy, who was shadow foreign secretary while Mr Raab was foreign secretary, told Sky News it was an “open secret” of bullying in his office. Mr Raab’s spokesman denied the allegations.