The Hutton inquiry into the death of Dr David Kelly enters a new phase on Tuesday, with witnesses being cross-examined by lawyers. One of the first witnesses to face potentially hostile questioning will be the deputy chief of defence intelligence, Martin Howard. He has previously described to the inquiry his involvement in the arrangements for dealing with Dr Kelly after he admitted talking to a BBC journalist. On Monday BBC boss Greg Dyke and the UK's top spy chief, MI6 director Sir Richard Dearlove, both appeared at the inquiry. Mr Dyke admitted the BBC had made some errors in its response to a story about the government's handling of intelligence about Iraq. And in an unprecedented "public" appearance via audiolink, Sir Richard admitted the claim in a government dossier that Iraq could deploy weapons of mass destruction within 45 minutes had been "misinterpreted". Mr Howard will be examined by lawyers for the inquiry itself, and by barristers for Dr Kelly's family, for the BBC and by his own lawyer. He is expected to be pressed over the Ministry of Defence's "naming strategy" for Dr Kelly, after the scientist had come forward as a possible source for a controversial BBC report on the dossier. Dr Kelly apparently committed suicide after being named in public as the suspected source. MoD press officer Kate Wilson will also be cross-examined on Tuesday. Three other witnesses who were unable to appear in the first stage of the inquiry are also due to appear, but will not be cross-examined. They are Detective Constable Peter Coe of Thames Valley Police, pathologist Nicholas Hunt, and Dr Andy Shuttleworth of the Defence Science and Technology Laboratory (DSTL). 'Hindsight regrets' Mr Dyke said the BBC had made a mistake in trying to reply too promptly to complaints from former Downing Street press chief Alastair Campbell about the dossier story. He said that, in hindsight, Mr Campbell's letter should have been passed to the BBC's complaints unit for a full investigation, rather than being dealt with at speed by management. But Mr Dyke said news bosses had felt they had to react after Mr Campbell staged an "unprecedented" attack, accusing the BBC of bias over its entire coverage of the Iraq war. Mr Dyke also criticised Today programme correspondent Andrew Gilligan for sending an e-mail, to an MP sitting on a Commons committee investigating broadcasts about the Iraq dossier, which revealed Dr Kelly as the source of a colleague's story. The BBC chief also admitted defending the report without being aware of the wording of one of the broadcasts, nor of an e-mail from Today editor Kevin Marsh, which described it as "flawed". Critical of Dr Kelly Sir Richard Dearlove said the 45-minute claim - reportedly criticised by Dr Kelly - had been a "piece of well-sourced intelligence" from an established, reliable source. He conceded the claim may have been misinterpreted by the public, but said he had not been aware of any unhappiness about it from members of his staff. He agreed that, in hindsight and with the interpretation the public gave the claim, it could be argued it had been given undue prominence in the dossier. "But I am confident that the intelligence was accurate and that the use made of it was entirely consistent with the original report," he said. Sir Richard said the original intelligence report had referred to battlefield weapons, but the claim in the dossier had been interpreted by readers as referring to long-range weapons. Sir Richard also criticised Dr Kelly for things he said in his conversation with BBC Newsnight journalist Susan Watts. "I am shocked to see someone discussing one of the intelligence reports without authorisation. It is a serious breach of discipline," he said. **PHOTO CAPTION*** Weapons expert David Kelly's spiritual mentor, Mai Pederson, will issue a statement about her relationship with the dead government scientist. (Thames Valley Police/HO)