Mr Delaney said the plane's fuel caused the fire that lit up the fence and also set part of the house on fire.
Witnesses heard the plane's engine stall before it crashed into the house and caught fire about 1.25pm (AEDT) today, Acting Inspector Janene Denton said.
"We're told by witnesses that there was a stall of the engine of that plane and it's come down and collided with the corner of a house, and ended up in a laneway behind that house," Acting Insp Denton told reporters.
The single-engine light plane, which was travelling south along the Chelsea foreshore, may have been a homemade aircraft, Acting Insp Denton said.
Witness Ashleigh Benson saw the light plane drop steeply in a "nosedive" before it crashed.
"This big thing of smoke came out, you could see it from about 10 minutes up the road," Ms Benson told AAP.
Megan Johnston was working in her office when she heard the plane go down.
"I heard the plane engine starting to splutter and it sounded very close," Ms Johnston told AAP.
"Then I obviously heard a massive explosion."
She ran around the corner to see an elderly woman standing in shock outside her house, which was starting to catch on fire.
"There were flames on the outside of the house and there were flames just starting to lick the kitchen," Ms Johnston told AAP.
"The house was full of smoke basically. A lot of really thick, black, toxic smoke."
Ms Johnston said the woman told her there was no one in the house except for her cat, so she went inside to try to find it.
"The lady's kitchen was just like literally a bomb had gone off," she said.
"I just kept going up and down the stairs trying to locate her cat, but I couldn't stay up there for long because of the smoke."
Dave Forrest was at work when he heard the plane go down, and was one of a few people who tried to put the fire out.
He said he found a hose and fed it out while someone else tried to douse the flames.
Mr Forrest said he spoke to the woman from the house and said she seemed to be in shock.
"I could see she was pretty stressed," Mr Forrest told AAP.
The woman inside the home was not injured, Acting Insp Denton said.
She said debris was spread along the Chelsea beach and warned locals to be careful.
- AAP