Officially, the Government insists that the dramatic expansion of the European Union will have only a negligible impact on Britain.
An academic study commissioned by the Home Office concluded that between 5,000 and 13,000 economic migrants from Poland, the Czech Republic and the other eight EU "accession countries" would travel to Britain.
Privately, however, ministers admit the prediction is a stab in the dark, based on the experience of previous EU expansions, notably the admission of Spain and Portugal in 1986.
There could also be a serious flaw in the research as it failed to take into account the decision by France and Italy - which could have been popular destinations for migrants - to impose border controls.
In addition, ministers have been rattled by the decision of traditionally liberal Sweden, Denmark and the Netherlands to take a similarly tough line after the expansion on 1 May.
They fear that if Britain stands alone without a work permit scheme, it could become a magnet for economic migrants. For that reason they are keeping open the option of imposing work permits on citizens of the new entrant countries if the influx of migrants materialises.