"Ten seconds later there was a banging at the door and a fireman screaming that there was a fire."
The fire started at 0824BST on Wednesday morning at Arlington House in All Saints Avenue.
Nine adults and a child were rescued from the 13th floor of the 16-storey building.
It took 14 fire engines and 70 firefighters four hours to contain the fire which was described as a "major incident".
Smoke 'everywhere'
One eyewitness described being woken in her flat: "I got up and looked into the hall because I heard all the commotion.
"It was filled with smoke."
She added:"We went over to the window and saw firemen looking up at us and pointing.
"Ten seconds later there was a banging at the door and a fireman screaming that there was a fire."
The casualties have been taken to the Queen Elizabeth, the Queen Mother Hospital in the town.
They are suffering from the effects of smoke inhalation.
Three firefighters have also been taken to hospital with burns.
The other residents of the building were checked for injuries by ambulance crews and police.
A helicopter from RAF Wattisham in Suffolk was also used to check if anybody had climbed onto the building's roof.
Police have begun an investigation into the fire's cause.