My eye was recently caught by an article in the times about Migration Watch and David Coleman (not this, but similar, can't actually find the actual one). So what about these impartial statistics? Well one that was widely covered at the time was the claim that "the benefit to each member of the native population of the UK from immigration is worth about 4p a week - or less than the equivalent of a small Mars bar a month.".
So let's unpack that claim. Forget any sophisticated analysis the 4p figure is based purely on dividing the government's estimated additional GDP due to immigrants divided by the population + net immigration. According to Coleman it is GDP per head that counts, but is it? I think not for some pretty obvious reasons, reasons you'd think would be very obvious to a Professor of Demography. For a start many of these migrants are young and single (often Eastern Europeans) looking to make money to send home or to take home where the cost of living is lower - and thus with the implication that they will not remain in the UK long-term (remember the horror stories about how we don't have enough young working people to ay for healthcare and pensions for the old codgers - well here they are!).
Even if this were not the case these working young adults (unable to claim benefits) take up a disproportionately lower fraction of public spending than does your average Briton (who is quite likely to be old, sick or unemployed). So it seems like GDP per head is precisely the wrong measure of immigrant contributions to GDP, and you have to wonder in that case quite why those chose to focus on that figure rather than a different and more meaningful one.