Of those, five have been formally identified, police have confirmed.
Police Commander Stuart Cundy said: ‘We are supporting the families and loved one of each of those 79, and with the agreement of the families and the coroner once we have confirmed identities of those that have died we will be releasing their names.
‘Sadly for many families they have lost more than one family member and my heart truly goes out to them.
‘This is an incredibly distressing time for all of them and I’ve said before one of my absolute priorities is to identify people as quick as we can, and to recover them from Grenfell Tower.
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‘That number 79 may change. I believe there may be people who are in Grenfell Tower that people may not know are missing and may not have realised they were in there on the night.
‘Equally there may be people who thankfully managed to escape the fire and for whatever reason have not let their family and friends or the police know that they are safe.
‘If that is you or if you know of someone who escaped and we haven’t been informed, I don’t care what that reason is, but I urge you to get in touch.’
Mr Cundy pledged to carry out the rest of the investigation as quickly as possible, but reiterated that the devastation is so severe, it may not be possible to identify every victim.
‘The awful reality, as I’ve said before, is that due to the intensity of the fire and the devastation within Grenfell Tower we may not be able to identify everybody that died,’ he said.
‘We have been from the top to the bottom of Grenfell Tower.
The search operation will be painstaking. Having been in there myself its really hard to describe the devastation that the fire has caused.’
The devastating fire swept through the Kensington high rise in the early hours of 13 June.
Anger has risen since the disaster as it emerged that cladding added to the building during a renovation last year was not fire-proof.