"This new team is now leading the recovery and response to the Grenfell Tower fire, which has been one of the most tragic and horrendous events ever seen".
Mr Khan, who said it was "humbling" to attend the service, paid tribute to the community for its resilience but said a feeling of anger remains.
The PM has ordered a public inquiry into the blaze, as the cladding used to insulate the tower block and the building's safety measures have come under scrutiny.
George Brewis, 85, who has lived in nearby Aberdeen Tower for 50 years, said: "I felt bad for the people in London, it is so tragic".
Sixteen bodies have been taken to a mortuary, and the first victim formally identified was named as Mohammad Alhajali, a 23-year-old Syrian refugee.
Following the meeting, May released a strongly-worded statement in which she said on-the-ground support for families in the immediate aftermath of the blaze "was not good enough".
Nisha Parti, a film producer who has been helping organise help for victims of the fire in Kensington, revealed the local council is giving the measly sum to survivors when they are checked in to hotels.
A total of 58 people who were in the Grenfell Tower on the night of the fire were missing and presumed to be dead, London police Commander said Saturday.
May also said phone lines would be better staffed and more staff would be deployed in the area.
As they left Number 10, one representative spoke to reporters briefly, saying they had spoken to the prime minister for two and a half hours about their demands and what they expected.
They would wear high-visibility clothing so they could easily be found, dispense advice and ensure the right support is provided, she added.
The prime minister said the inquiry, which is expected to cost several million pounds, was needed to ensure "this awful tragedy is properly investigated" - however local residents are demanding an inquest.
She has told councils to complete urgent safety checks on similar tower blocks.
In an interview with the BBC, May promised a public inquiry into the disaster and pledged that survivors would be rehoused within weeks.
On Friday, she was heckled on a visit to the North Kensington estate, and protesters marching on Friday and Saturday called for her resignation.
After a botched snap election that lost her party its majority in parliament, May is facing criticism for her response to the blaze which engulfed the 24-storey apartment block of social housing on Wednesday, killing at least 30 people.
Victims of the Grenfell Tower disaster who have been left homeless will be given at least £5,500 from an emergency fund, Theresa May has announced.
Queen Elizabeth II and senior royals have marked her official birthday in the annual Trooping the Color celebration.
Michelle said the staff know every person living in the flats and anyone with a disability is never housed above the fourth floor.
The Hammersmith and City Line has been suspended between Edgware Road and Hammersmith, and the Circle Line is also closed, Transport for London said.