Benita Mehra tendered her resignation to Boris Johnson after fury and mounting pressure over what was said to be a conflict of interest.
She stepped down just two days before the resumption of the inquiry into the 2017 fire that killed 72 people, saying she recognised and respected the “depth of feeling” among some about her appointment.
Survivors of the disaster and bereaved families had threatened to boycott phase two of the inquiry on Monday.
Lawyers for more than 60 participants had also urged her to quit.
Earlier this month it was revealed that the engineer, who had been due to join the panel for the second phase of the inquiry, was a former president of the Women’s Engineering Society (WES). The society last year received funding from the Arconic Foundation for an apprentice conference.
Arconic supplied the cladding on the outside of the west London tower block, which went up in flames on 14 June 2017.
A report following the first phase of the inquiry concluded in October that the cladding did not comply with building regulations and was the “principal” reason for the fire’s rapid and “profoundly shocking” spread.
Grenfell United, a group for the bereaved, survivors and the community, said Ms Mehra had done the right thing in resigning, saying it “helped lift growing anxiety” before the next inquiry phase.
The group said questions remained over how the situation was ever allowed to happen, and that a new panellist must urgently be found. A spokesperson said: “We do not need the pretence of diversity for the sake of diversity.”
However, the Cabinet Office said it still believed there was no conflict of interest and she could have remained on the panel.
Trades union Unite had urged Ms Mehra to step down, citing “a conflict of interest”.
In a letter to her from the union, one of the victims’ relatives wrote: “I strongly disagree with her sitting on the panel and I personally, and many survivors and bereaved families, believe the inquiry should not start while she is appointed.”
Arconic said a “confluence of unfortunate circumstances” rather than the “mere presence” of the panels had caused the spread of the fire.
In a letter to Mr Johnson, Ms Mehra wrote: “As you know, I had hoped to draw on my experience and knowledge of the construction industry, of community engagement and of governance within housing management to contribute to the vital work of the inquiry in discovering how and why the devastating fire at Grenfell Tower happened.
“However, it is apparent that my former role as president of the Women’s Engineering Society (WES), which in 2017 accepted a charitable donation from the Arconic Charitable Foundation to support the mentoring of women engineers, has caused serious concern to a number of the bereaved, survivors and resident core participants.”
She said her role at WES had been unpaid, and the grant from Arconic was ring-fenced to fund the mentoring scheme.
“For these reasons, I did not link any aspect of my former role as president of the WES to my panel member role for the Grenfell Tower inquiry. In hindsight, this was a regrettable oversight on my part.”
Mr Johnson confirmed in a statement that he had accepted her resignation, adding: “I would like to thank Benita for her commitment and I am very grateful for her sensitivity to the work of the inquiry.
“As the inquiry’s phase two hearings begin, we remain completely committed to getting to the truth of what happened, learning lessons and delivering justice for the victims.”
A letter to Ms Mehra from the prime minister’s private secretary read: “It is clear that you offered your resignation out of respect for the bereaved, survivors and local community of the Grenfell Tower fire, and to ensure that the inquiry proceeds with the confidence of all parties.
“I note that the Cabinet Office, having made further inquiries into your case, have said that they continue to believe that there is no conflict of interest that would have prevented you from taking part in the inquiry.”
Additional reporting by PA