However James Brokenshire, a Home Office minister, yesterday suggested said that the Home Office is "working on" the idea of appointing a co-chairman.
Asked about the idea, he said: "Well I think it’s this precise detail that we are working on at this stage because it is important that we do draw on the right experts.
"This is something that will be an inquiry that will go on for some time, we’ve said that it should have an initial response by the time of the next general election to inform the incoming government and to be able to update parliament and the public
"Our expectation is that it will flow though and beyond the next general election given the very detailed and broad range of its remit."
He added, however, that Baroness Butler-Sloss's integrity "shines through" and that she has been an "incredible advocate" for children's issues.
Yvette Cooper, the shadow home secretary, suggested that the scale of the investigation – which is examining the Government, the NHS, the church and the BBC – may mean it needs a co-chair.
She said: "Well I think that’s going to be a matter for the Home Office to work out what will best actually command the confidence that we need in this because bear in mind, there are a series of things that have got to be got to the bottom of. There’s the police investigation into any allegations of abuse against children, there’s got to be that criminal investigation."