Basildon Hospital is already under investigation for its high death rates, it is now being examined for its treatment of a disabled woman.
The health watchdog says Tina Papalabropoulos died after doctors failed to provide her with intensive treatment.
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"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.