This may sound like bizarre behaviour on the part of the headteacher of Camden School for Girls. But when your school is as popular as this one, and parents are pulling elaborate wheezes to gain admission, you have to be vigilant.
The school's deadline for accepting pupils for the autumn term falls at the end of this month. Once a child has been accepted, parents are free to move miles away from the school and younger sisters also win the right to a place. So Mr Fallows has to do his homework now. His dilemma finds echoes all over Britain, wherever the best state schools are oversubscribed.
Mr Fallows remembers a couple who claimed that their marriage had broken up, and that the children were living with one parent in a flat near the school.
"I had my suspicions," he says. "So I knocked on a few doors and asked the neighbours if there were any children living there. My inquiries led me to decide not to admit the daughter. It seems that the family was living miles away. They threatened to fight me through the courts and complained about the fact that I'd been asking questions. But they subsequently did nothing and I took that to be an admission of guilt."
Many parents find God, if temporarily, in order to secure a place at a church school. Others simply forge their addresses. One west London couple who had recently split up applied to a London comprehensive miles from where they lived. On their application, they used the address of a flat belonging the husband's new girlfriend. Letters which went out from the school duly received replies. No one ever suspected the ruse.
In the eyes of the authorities, such parents are cheating, although they are content to see parents move house to get within the catchment area of a good school.
But a clampdown could be imminent: the Local Government Association wants parents who caught out cheating to be fined pounds 2,000 - the cost of a year's schooling to the taxpayer. Parents desperate to get their children into good schools are unlikely to be deterred, however. Angelina's parents tried to find places for her in good state secondary schools all over north London. No luck. "I was determined to find her a good school," says her mother. "Eventually, I told her that she would have to go and stay with her grandfather, who lives just around the corner from an excellent school. She stayed there for a few weeks through the admissions process, and got a place." Once admitted, Angelina returned to her home.
Angelina, who has since achieved good exam results, says the consequences for those friends who did not commit such frauds have been dramatic. "My best friend lived only 10 minutes away from my school. But she didn't get a place. She had to go to a school which was so bad that eventually her parents sent her to a boarding school in Ireland."
Another woman pulled a different scam. She had problems finding a place for her child in a primary school serving the rich London suburb of Hampstead. The child's name had been on the waiting-list since the age of two. But by the time he was five, no place was forthcoming. "Eventually," says a friend, "she persuaded someone with children already at the school to say that they were cousins. That did the trick."
As schools catch on to parents' scams, the cheating gets increasingly desperate. One parent from north London failed to find a good school for her daughter, who was stuck in a failing comprehensive. A friend explains: "She found a counsellor and went along for a few sessions with her daughter. She got her daughter to tell the counsellor how traumatised she was at her new school, how she was being bullied, and so on. I know she manufactured this story. But she persuaded the counsellor to appear at an appeal for her. And that was that. She got her place at the school she wanted."
Some names have been changed