It predicts this level annually in the first five  years after these controls end, warning of “significant consequences”  for housing and jobs, the BBC reports.

Citizens of both countries will have free movement across the EU in 2014.

Ministers say calculations are difficult but the Home Office said it was working to cut net migration.

Prime Minister David Cameron said earlier this week the detail for such calculations “wasn’t there yet”.

The Home Office said it wanted to move from hundreds  of thousands to tens of thousands of migrants by the end of this  Parliament.

From next year, like other EU citizens, Bulgarians  and Romanians gain the unrestricted right to live and work in the UK  where currently, they require authorisation before taking a job.

Migration Watch, which supports tighter immigration  controls, said its study suggested its estimates could be considerably  higher if there were to be a movement of Roma people to the UK or if  some of the nearly one million Romanians resident in Spain and Italy  moved to Britain.

It said Germany and the Netherlands were “likely  destinations” for Romanian and Bulgarian migrants because their youth  unemployment rates were lower than other EU countries.

But it said the UK, with youth unemployment at 20%,  “is nonetheless an attractive destination, partly because of its  flexible labour market and partly because of the ease of access to its  benefits system”.

Sir Andrew Green, chairman of Migration Watch said:  “It is not good enough to duck making an estimate of immigration from  Romania and Bulgaria. It is likely to be on a scale that will have  significant consequences for housing and public services.

“It will also add further to the competition which young British workers already face.

“We have therefore produced our own estimate as a  contribution to an important debate which must include the ease with  which migrants to the UK can currently access the welfare state.”

It analysed migration from other European countries  and the number of Bulgarians and Romanians already in Britain before  making its estimates.

Sarah Mulley, of the Institute for Public Policy  Research (IPPR) think tank said that although it was “very difficult to  predict migration flows with any degree of confidence in these  circumstances” the estimates put forward by Migration Watch “look high”.

She said: “The UK is opening access to its labour  markets along with the rest of Europe and the process of opening up to  Bulgaria and Romania has been a gradual one, in contrast with 2004 when  the UK was the only large EU country to open its labour market and when  borders and labour market access were opened at the same time.

“So it would be very surprising if net migration from Bulgaria and Romania was on the scale predicted by Migration Watch.”

Temporary curbs on Romanian and Bulgarian migration  were imposed by the Labour government in 2005 to protect the UK labour  market.

The Labour Party has said it would support any moves to extend the measures.

But Home Secretary Theresa May said in November  temporary curbs could not continue under EU law and the government was  looking instead at limiting access to benefits and the NHS to reduce the “pull factors” that encouraged migrants to come to the UK.

Last weekend, Communities Secretary Eric Pickles  warned an “influx” of Romanians and Bulgarians would add to the existing housing problems in the UK.

But he refused to give an estimate of the numbers of  people who might move to Britain after getting the right to live and  work in the UK in December, saying he did not want to start a “scare  story” and that more work had to be done on drawing up a robust figure.

The government’s migration advisory committee has  also said there is evidence that Bulgarians would move to Britain  because of its stronger economy, and it was “plausible” Romanians would  come for the same reason.

The Home Office said: “We are working to cut net  migration from hundreds of thousands to tens of thousands by the end of  this Parliament and our tough new rules are already taking effect with  overall net migration falling by a quarter in the past year.

“In terms of European immigration, we are working  closely with other government departments to look at the pull factors  that may encourage EU nationals, including those from Bulgaria and  Romania, to come to the UK.

“The government has made clear it will always apply  transitional controls on new EU member states and will continue work to  cut out abuse of free movement.”