Rev Mike Long spoke after the first hearing in the investigation, chaired by retired judge Sir Martin Moore-Bick (pictured above), got underway last week.
Speaking with Premier, he said: "Some people are significantly upset that the inquiry panel doesn't include someone from the local community... but I do think there's a range of emotions around this and, perhaps, it depends on how close people are to the situation".
Former Court of Appeal judge, Sir Martin was heckled during a meeting attended by survivors and bereaved families on Wednesday when he promised that his investigation would "provide answers".
Rev Mike Long at Notting Hill Methodist Church - a short distance away from the scene of the deadly tragedy on 14th June which claimed at least 80 lives - said people are "relieved" the public inquiry has begun and are hoping for transparency.
Asked if he believes the probe will address the concerns of residents, the minister answered: "I think it will depend on how the inquiry proceeds, the line of questioning and the extent to which the inquiry really is trying to dig deep as to the causes of the fire - by that I don't just mean the technical aspect."
During Wednesday's 45 minute hearing, Sir Martin said he would not "shrink" from making conclusions that could affect criminal prosecutions or civil actions, if necessary.
Rev Long explained what would help the community through its grieving process, explaining: "Clearly, some common acceptance that truth is being done and is seen to be done will help significantly in that process.
"That's why the outcome of the public inquiry and the way's it's being conducted is so important here."
Premier has contacted the Grenfell Tower Inquiry for a response.