Home Secretary Theresa May will have a "tough job" to replace Fiona Woolf if she steps down as head of the Westminster sex abuse inquiry, the former director of public prosecutions said.
Lord Macdonald said if that happened it would be difficult for May to persuade someone else to take it on.
Woolf is the second person appointed to head the inquiry into the historical allegations.
Baroness Butler-Sloss stepped down from the role in July following concerns about her family links.
Her late brother, Sir Michael Havers, was attorney general in the 1980s when the abuse is said to have taken place.
A 53-year-old man has been arrested in connection with a blaze at a fireworks warehouse, Staffordshire police said.
Police also said that they now believe two people rather than one remain unaccounted for as the investigation continues today.
Murderers Jamie Reynolds, a "sexual deviant" who lured a teenage girl to her death, and former soldier Anwar Rosser, who savagely killed a child, have lost Court of Appeal challenges against orders that they can never be released from prison.
Fiona Woolf is "unqualified" to lead an inquiry into alleged sex abuse in Westminster in the 1980s, critics say.
Pete Saunders, chief executive of the National Association for People Abused in Childhood, said the government should appoint "somebody credible" like 'radical' lawyer Michael Mansfield QC.
Mansfield is said to be the 'abuse victims choice' and has represented the families of Jean Charles de Menzes, shot dead by police in 2005, Mark Duggan, whose death sparked the London riots, and victims of the Hillsborough disaster.
Mr Saunders told BBC 4's Today programme: "If you're going to put together an inquiry into this massive problem, then surely you would appoint a group of specialists who know something about the subject and will have the confidence of the people who are suffering from that particular issue.
"Nobody is having a pop at Fiona Woolf as a person - I'm sure she's a person of high integrity - but she has no qualification whatsoever to lead an inquiry into such a deeply, deeply disturbing issue as child abuse.
"She has said as much, so why should we appoint somebody (like that)?"
Alleged victims of a Westminster sex ring want the new head of the inquiry into the claims to quit.
Lawyers for them will call for Fiona Woolf's resignation at a government meeting later today.
It comes after lawyer and Lord Mayor of London Woolf allegedly played down her connections with former Cabinet minister Lord Brittan and his wife.
Lord Brittan is accused of failing to act on the abuse allegations despite being handed a dossier of evidence when he was in office in the 1980s.
A second pilot over the past three days has been arrested over concerns about alcohol levels in his body. Ian Jennings, 47, from Gale Moor Avenue, Gosport, Hampshire, was arrested at Norwich Airport yesterday afternoon after landing a private plane.
He has been charged with performing an aviation function when the alcohol in his breath was over the prescribed limited, Norfolk Police said.
Jennings was released on bail to appear at Norwich Magistrates' Court on November 13 where he will face the allegation under the Railways and Transport Safety Act 2003.