We need to know what happened, we need to have an explanation of this.
Barrister John Cooper QC, who is representing some of the victims of the Grenfell Tower fire, told Julia Hartley-Brewer: "Two of the most important aspects of an inquiry is one, to make recommendations which are followed through to make sure lessons are learned, and two, to hold people to account".
Many of those who lost their homes are still waiting for a new one.
"The inquiry cannot undo any of that, but it can and will provide answers to how a disaster of this kind could happen in 21st Century London".
Moore-Bick's announcement that no community members would be included in his team of assessors, because it would risk undermining his impartiality, disappointed residents and community activists.
Demonstrators gathered outside the building where Sir Martin made his address carrying banners that read: "Justice for Grenfell".
Moore-Bick has said he expects to publish an interim report by the end of March or the beginning of April.
A video stream was also set up at Notting Hill Methodist Church close to Grenfell Tower.More news: International Olympic Committee crowns Paris 2024, Los Angeles 2028 in unique double
Police say at least 80 people died in the inferno, however some residents believe the real figure is higher.
The inquiry will examine the actions of Kensington and Chelsea Council.
The inquiry will focus on the cause of the fire and why it spread so rapidly, high-rise building regulations, and how local authorities responded in the aftermath of the June 14 blaze. This decision is notable due to the criticism the ex-judge faced for excluding a wider examination of social housing policy.
Commenting on the scope of the inquiry, Sir Martin said: "The terms of reference are deliberately broad in scope to allow me to pursue relevant lines of enquiry".
"I wish to emphasise that the inquiry is not limited to factual questions surrounding the development of the fire. That will be an integral part of understanding how and why this fire occurred".
Labour MP for Kensington Emma Dent Coad said they needed somebody they could trust, not a "technocrat" who lacked what he called "credibility".
Residents had complained for years about fire safety in the 24-storey social housing tower and have voiced anger at delays in assistance following the blaze as well as scepticism about whether the inquiry can help.
And seven in 10 blocks have only one staircase for evacuation, according to the shock results of a BBC Breakfast probe covering half of Britain's council and housing association-owned towers.