Writing in the Observer, Mr Khan it may well be the "defining outcome of this tragedy that the worst mistakes" of that era become a thing of the past.
Thirty people have been confirmed dead following the devastating inferno in north Kensington, with a further 28 missing presumed dead.
Mr Khan said the images of the 24-storey building being ravaged by fire "should be forever seared into our nation's collective memory".
He said: "Little can compare in recent times to a tragedy on this scale - the response from the local authority has simply not been good enough. Residents feel abandoned by those with the power - the council and government.
"This is a national tragedy with national consequences. What emerges in the coming weeks and months will be very difficult for many people, including politicians and organisations, but we must get to the truth.
"Those who mock health and safety, regulations and red tape need to take a hard look at the consequences of cutting these and ask themselves whether Grenfell Tower is a price worth paying."
Mr Khan said an inquiry should be properly resourced so it can get the full truth about the fire as quickly as possible.
He said: "The greatest legacy of this tragedy may well end up being the skyline of our towns and cities.
"Nowadays, we would not dream of building towers to the standards of the 1970s, but their inhabitants still have to live with that legacy.
"It may well be the defining outcome of this tragedy that the worst mistakes of the 1960s and 1970s are systematically torn down."