Police believe the attack may be linked to a recent campaign by the News of the World newspaper to name convicted sex offenders.
Roy Reynolds, who is now serving a life sentence in prison for child abuse, once lived at the flat. The family are unrelated to him.
He said: "Someone may well have set fire to the flat thinking Mr Reynolds was in there. He wasn't.
"This is clearly a case where something tragic could have happened to a father and three young children."
Not named
The father and the children, all under three years old, were woken by the smell of smoke when someone pushed a roll of burning paper into the flat and set fire to the floor.
They escaped unhurt from the fire.
The News of the World told BBC News Online that Reynolds was not one of those named in their campaign, but refused to comment further on the incident.
There have been a number of protests against suspected paedophiles and attacks on innocent people following the paper's campaign to "out" 110,000 convicted sex offenders.
It called a halt to the campaign, which was started after the murder of Sarah Payne, after mass criticism from the police and children's charities.
The paper is now calling for authorities to be given more powers to deal with sex offenders, including the right for parents to have access to lists of child abusers.
Last month a paediatrician in Newport, south Wales, was forced to flee her house when vandals seemingly confused her job title.
The word "paedo" was daubed on the front door of Dr Yvette Cloete's home.
Tough police powers
Home Office Minister Mike O'Brien said the government was planning to give police strong powers to protect children.
"We are looking at very tough police powers to deal with paedophiles," Mr O'Brien told GMTV's Sunday Programme with Alastair Stewart.
"We are looking at the detail of the review that we've already announced into the sexual offences legislation, and we will be announcing in due course that we will move forward to deal with the public concern, that we need to have a very tough line to protect children.
"We will protect children against paedophiles."