Several news outlets (including the BBC) today covered figures published by think tank MigrationWatch suggesting that “over the next five years – to 2016 – 550,000 more school places will be needed as a direct and indirect result of migration”.

The report claims that this would rise to over a million by 2020, and makes longer-term predictions about the number of children who will be born in Britain as a result of immigration.

These figures are used to estimate the costs of educating the children of migrants, including a widely-reported figure of £40 billion over the next five years.

The report, though short, incorporates a labyrinth of calculations based on figures from various sources, some of which use numbers included in the report, while others do not.

The claims are apparently based on several sets of data from the Office for National Statistics (ONS), one showing the number of children born to foreign-born parents in recent years and another projecting population change between 2008 and 2033.

Though the report takes great pains to explain its methodology, it does not include data going back beyond 1998, which is essential to their figures. For example, a projection for the number of students born to foreign parents in the school system in 2013 would need to take account of children born in 1997.

Moreover, MigrationWatch say that their figures are based on “the ‘principal projection’ by ONS of UK population over the period 2008 – 2033, projects a total of births of 19.8 million, of which 2.3 million are projected to occur, directly or indirectly, because of net migration”.

But after much searching and head-scratching, Full Fact was unable to discover any ONS projections which broke down predicted birth rates by the parents' place of birth.

A call to the ONS confirmed that no such statistics exist: “"We certainly don't publish population projection data by country of migrant or any kind of ethnic background,” said a spokesperson, “the sums themselves won't have been done by us.”

This projection, then, must have been arrived at by MigrationWatch using figures from the ONS.

Which figures, and how they were used, is something that only MigrationWatch can tell us. We have contacted them, and hope to update with the response we receive.

Meanwhile, there are a few further reasons why the MigrationWatch analysis should be treated with caution.

Firstly, as the report admits, it is not standard practice to take into account children born to one UK-born and one foreign-born parent, which the report he authored does. It is not for Full Fact to judge whether MigrationWatch or the Home Office are right on this issue, but the difference it makes to the final figures is significant.

Secondly, the fact that running totals are used mean that any errors would be amplified over time.

Finally, the cost calculations are a gross figure. They do not take into account the tax contributions of immigrants, which fund the state education system that the report assumes will shoulder the cost.

For a fully informed verdict on the MigrationWatch figures, however, we await clarification over their sources.