British Prime Minister Theresa May apologised on Wednesday for the state's failure to support those people who survived the massive London tower block fire, and the government secured its first tranche of new homes for displaced residents.

The government said it had obtained dozens of newly built apartments in a west London development, a first step towards fulfilling a pledge to rehouse residents of Grenfell Tower which was gutted in a deadly fire.

May took responsibility for shortcomings in the response to the fire a week ago, and pledged that victims would receive more support.

"The support on the ground for families in the initial hours was not good enough... That was a failure of the state, local and national, to help people when they needed it most," she told parliament on Wednesday.

"As prime minister, I apologise for that failure and as prime minister, I've taken responsibility for doing what we can to put things right."

May added that those who had lost their homes would receive a downpayment from an emergency fund, and repeated a promise to rehouse all victims within three weeks.

Communities minister Sajid Javid said that 68 apartments were newly built social housing in Kensington Row, where private properties can cost as much as 3.5 million pounds ($4.43 million). He added that these were the first batch of permanent new homes to rehouse residents of Grenfell Tower.

Police said that 79 people were dead, or missing and assumed dead, after the blaze rapidly spread through the 24-storey block. The tragedy shone a spotlight on London's economic divide, as it happened a few hundred metres (yards) away from one of the wealthiest neighbourhoods in the country.

The upmarket neighbourhoods of London's Kensington district have proved hugely popular with foreign buyers in recent years, and pressure had been growing to ensure that victims of the fire were not relocated outside of the borough when many properties nearby stand empty for much of the year.

Opposition Labour party leader Jeremy Corbyn has called for government to requisition unoccupied properties in the area to rehouse residents.

Properties for sale on Kensington Row are priced between 1.5 million and 3.5 million pounds, according to housebuilder Berkeley Group's website. The development is just a mile away from Grenfell Tower.

The government said that the new homes will be a mix of one-, two- and three-bedroom flats across two blocks, and that developer St Edward was committing extra staff to the project to fast-track its completion.