So, that's all from us for now. Our live coverage is over but we'll continue to cover any important developments on our news site.
Home Affairs Correspondent
Unlike Sir Martin's previous public appearances - when he was heckled by people who survived the fire or live near the tower - his opening statement was heard in silence by Grenfell residents and the bereaved.
But there's still a lack of trust among local people of a process launched this morning at the lavish London Connaught Rooms.
They described Sir Martin as an establishment figure presiding over a public inquiry surrounded by gold leaf.
Outside, the inquiry's critics told us they were angry at his decision not to appoint survivors as part of a team of assessors who will advise him.
The judge says that could damage his impartiality.
Sir Martin's speech focused on his strategy for keeping what could be become a mammoth inquiry on the rails - this includes splitting it into two phases.
The second, which looks at how the refurbished tower ended up a potential death-trap, could be the more complicated.
Sir Martin said the reasoning behind decisions about the tower's management will be a key area of investigation.
It is likely to look at whether cost-cutting led to to fatalities in Britain's worst ever tower block fire.
- Copyright: BBC
Labour MP for Kensington Emma Dent Coad is highly critical of the choice of venue - the Grand Connaught Rooms in central London - a long way from the tower.
"We were sitting in a ballroom, dripping with chandeliers. It's the most incredibly inappropriate place," she tells the BBC.
"Clearly, the judge felt perfectly comfortable in a place like this - a lot of people didn't."
People feel it was deliberate, to intimidate and make people "feel unimportant and looked down on", she adds.
Sir Martin was clear in his statement that the inquiry would not be held at that venue, and his team were seeking a larger venue.
Missed any of it? Read Sir Martin's statement in full here.
- Copyright: BBC
Joe Delaney, who was evacuated from his flat near the base of the tower, says Sir Martin "took a stumble today".
He's concerned that witnesses won't be cross-examined in the inquiry, and says there were "certain people representing groups who I wouldn't want to be speaking on my behalf".
He says he went into the inquiry feeling cautiously optimistic, but came out feeling "more cautious than optimistic".
Of the timetable to produce a first report by Easter, he says: "We don't need some meandering inquiry that's going to take years and doesn't get to any answers."
Sir Martin's opening statement was streamed to a big screen at the Notting Hill Methodist Church.Copyright: PA
BBC NewsCopyright: BBC
Hamid, who lived on the 16th floor of Grenfell Tower, watched Sir Martin's speech but left feeling he'd learned very little.Quote Message: We are waiting for the answers. We still need a proper answer. We just want to ask some questions but no chance. That didn't happen."
He says he is still living in a hotel three months on. "I want to get on with my life," he tells the BBC.
Speaking afterwards, Mr Mansfield tells the Press Association he had hoped to ask for a further meeting between Sir Martin and core participants, and said the manner of his departure was "disrespectful".
"I was making a request on behalf of survivors for another preliminary meeting when they would be there as key participants - as they are all going to be core participants - with designated lawyers, to sort out reservations and concerns that they have had from the beginning about this whole process."
More detail is coming in on what exactly happened at the end of Sir Martin's statement.
Michael Mansfield QC, who works with some of the survivors, said: "Sir, before departing, I wonder if I may make a quick request on behalf of survivors."
He was ignored by the judge as he exited the room to shouts of "hello?" and "rubbish" from gathered residents.Copyright: BBC
Reacting to the news that no survivors of the fire will be on the inquiry panel, Labour MP David Lammy says:Quote Message: The families are key and he has to walk and travel with them - follow the evidence, and be uncompromising in his search for it. He's said and he's indicated that that is what he intends to do."
Ismet Rawat, from the organisation BME Lawyers 4 Grenfell, said she would prefer a wider scope to Sir Martin's inquiry.
She has been calling for a two-stage inquiry, one looking at what he's described as phase one and phase two, as well as a second stage, looking at issues around social housing and austerity.Quote Message: This is not a fire that happened in a vacuum. There's a huge context. If it's left outside of this inquiry, we're concerned that it won't happen at all."Copyright: BBC
- Quote Message: As the inquiry begins, we're confident it will get to the truth of what happened and learn the lessons to stop a similar catastrophe happening in the future."
BBC Radio London Political Reporter
When Sir Martin Moore-Bick finished up, he and the inquiry team walked out of the room without taking any questions.
A few members of the audience called out to him as he left.Copyright: BBC
A small number of demonstrators held placards up outside the Grand Connaught Rooms.Copyright: Reuters
Sir Martin says it may feel that not much progress has been made since the fire, but it has.
The process of gathering evidence has already begun in earnest, he says.
But there are many witnesses still to be interviewed and documents to be reviewed.
He says he wants to start taking evidence before the end of this year, but that depends on how long it takes to obtain statements from witnesses of the fire.
The interim report, which he plans to publish by Easter, will be limited to the first phase of the inquiry, he explains.