Thousands of people have been donating to Claire Squires Just Giving page.
The thirty year old collapsed and died during yesterday's London Marathon.
More top news
"I do not accept the allegation that I have brought the Labour Party into disrepute", said Livingstone.
Family and friends of the victims of Grenfell Tower have been paying tribute to those who perished in the disaster.
The balmy conditions have swept in on a high pressure system, dragging in hot air from the continent, according to the Met Office.