Police said four of the injured were taken for treatment by ambulance, while four others arrived at hospital asking for assistance.
The two police officers were treated for the effects of smoke inhalation.
A London Fire Brigade spokesman said the fire appeared to have "spread very rapidly".
About 75 firefighters remain at the scene damping down. Fire crews are expected to remain at the scene for the remainder of the day.
A local resident, identified only as Elizabeth, was one of those who had to leave her home.
She told BBC London 94.9FM: "We just woke up into this total blaze from the construction site across the road and we were told to leave.
"The whole place was in pandemonium.
Evacuated people are being looked after by the council and Red Cross
"There was flying debris all over the place and there were cars ablaze and we were told to get out of the area."
John Osagie, 31, said he saw the fire when he came back from work in the early hours.
He said: "I stood there and waited for the fire brigade to turn up. They tried to stop it but it was getting worse and worse. Then they evacuated everybody.
"I was scared and I had to take some of my stuff and come and stand out in the cold."
He said he did not know whether his home had been damaged.
The fire, which began on a development where 39 flats were being built, has damaged property and buildings in Sumner Road and Rosemary Road.
Paul McKenzie, the owner of the Golden Lion pub which has been gutted, said: "I opened the fire door into the club room and it was just hot.
"The glass in the windows were cracked and I thought, 'You know what, this not somewhere you want to be'."
Some 260 residents are being housed in temporary accommodation provided by Southwark Council and a rest centre has been opened at the Damilola Taylor Centre, East Surrey Grove.
A number of properties have been damaged
Inspections are taking place to assess whether some residents can return to their homes on Thursday night, the council said.
People have offering support and donations such as clothes and toys, the council added, and these can be taken to the Damilola Taylor Centre.
A telephone helpline has also been opened for residents who require assistance, on 020 7939 3670.
The cause of the fire is not known at this stage.
It comes nearly five months after six people died when a fire destroyed the Lakanal House block of flats in nearby Camberwell.
Harriet Harman, the Labour MP for Camberwell and Peckham, said the same emergency services workers who tackled that fire were dealing with the latest incident.
Ms Harman said: "They were thinking 'no, not again', but I think we're really hopeful that there are no fatalities, that's our first concern, and our second is to help people who are in a state of shock.
"We have to make sure that people are re-housed and they are helped to just get on with their lives."
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