Nick Myatt of the London Fire Brigade has said the fire in a block of flats is under control.
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The 20-year-old was stabbed after the party was gatecrashed after details were posted on social media.
Incident commander Andrew O'Loughlin said the fire was exceptional but it looked as though it had "possibly done its worst" when he arrived.
The ambulance arrived a minute after Weihong Yu gave birth in Camden.