Last month, Hackney, one of Europe's poorest areas, became the first council to see key education services put out to tender.
But Colin Alston, head of research at Hackney, has found the borough would leap up the table from the fifth worst place if the thousands of transient pupils, many of them refugees, were removed from the calculations.
His study, reported in today's TES shows that settled pupils - those who stay at the same Hackney primary school from Reception to Year 6 - do significantly better than the borough average. Many of the mobile, mid-term entrants are economically disadvantaged and a high proportion have English as an additional language.
At key stage 1, one in five of Hackney's seven-year-olds had not been at the same school for the full KS1 curriculum. One in three of the Year 6 pupils had not been at the same school for the full four years.
The pupils' test results for 1998 mirrored closely the amount of time they had spent in the same school. Those who had arrived in Year 6 - the same year they were tested - fared badly.
"The LEA has to untangle the complex web of pupil mobility and its effect on the performance of schools," says Mr Alston.
Peter Robinson, senior economist at the Institute for Public Policy Research, said such findings added "another large question mark" to the use of league tables.
"Everyone recognises that there is a certain level of crudeness about those measures so we have to be careful how we use them to judge how successful a school is," he said.
Dr Janet Dobson, of University College London, who is carrying out a study on the effects of pupil mobility, said the Hackney research was probably the first of its kind, and called into question comparisons made between authorities - especially inner-London boroughs.
She said: "We need to change our whole perception of schools. We talk about them as though they were a stable situation."