The influx of Romanians and Bulgarians would add to the existing housing problems in the UK, Communities Secretary Eric Pickles has said.
He told the BBC's Sunday Politics that nobody knows the numbers of Romanians and Bulgarians who might come to Britain after getting the right to live and work in the country in December.
"I don't think anybody knows," he told the BBC.
Temporary curbs which were imposed on Romanians and Bulgarians in 2005 to protect the British labour market, expire in December. The curbs cannot be extended.
Asked how many Romanians and Bulgarians he expected to move to the UK, Mr Pickles said: "The truth is I don't think anybody entirely knows the number that will come from Bulgaria and Romania."
He said he had had "no discussions with the Home Office with regards to the numbers".
But he said individual councils were taking action to prepare for a possible large increase in the numbers of people moving to the UK from the two countries next year.
"We do know of a number of boroughs that have a higher than average number of Romanians so I would expect to see influxes in the east of London, which is predominantly where they are now," he said.
Mr Pickles added: "Given that we've got a housing shortage, any influx from Romania and Bulgaria is going to cause problems – it's going to cause problems, not just in terms of the housing market but also on social housing markets."