It could take 20 or 30 years to build enough social housing for illegal immigrants in Britain if they received an amnesty
The government has estimated the UK has up to 570,000 illegal immigrants.
MigrationWatch UK says granting them all an amnesty would put too much pressure on council housing.
But ministers say they have no plans for an amnesty, and supporters of the idea say it is misleading to blame immigrants for UK housing problems.
The MigrationWatch report says the number of asylum seekers granted permission to stay in the UK in recent years has exceeded the number of new social houses built in the same period by nearly 50,000.
Sir Andrew Green, chairman of the group, said: "The fair allocation of social housing is extremely difficult to achieve at the best of times.
"When you add in the unprecedented rise in asylum seekers granted permission to stay here in the last few years and then consider an amnesty against a background of low levels of construction, there is a real risk of harming social cohesion."
Sir Andrew said applicants who are granted asylum or exceptional leave to remain in the UK become eligible for social housing.
They did not get automatic access to social housing but it was likely the circumstances of people involved, particularly those with families, meant they would get high priority, he said.
Building every illegal migrant a house 'would take 30 years'