By Dominic Casciani
BBC News home affairs
The Home Office added that a further 49,000 workers from eight other Eastern European countries, which are already in the EU, applied to work in the UK.
More than 640,000 workers from Eastern Europe have sought work in the UK since the EU expanded in May 2004.
The government has restricted rights for Bulgarian and Romanian workers.
Romania and Bulgaria joined the European Union in January 2007 - but the government decided not to allow its workers free access to the British labour market.
The UK was one of the only countries to allow free access to its labour market for the eight European nations including Poland that joined in May 2004.
According to the government's figures, between January and March 7,935 workers from Romania and Bulgaria were granted permission to arrive.
Some 5,075 were allowed to apply directly for jobs, 2,660 registered as self-employed and 2,425 arrived as seasonal farm workers. Two hundred who arrived said they were self-sufficient.
Half of the applicants were between 25 and 34 years old. Six out of every 10 applicants came from Romania. Almost a third of the workers went into the entertainment and leisure industry.
Figures also show an increase in workers arriving from the eight Eastern European nations which joined the EU in May 2004.
While it is unclear how many of have settled for the long-term, the proportion of registered workers with children has risen from 4% in 2004 to roughly 10%.
In total, there were 49,000 initial applicants to the government's scheme for Eastern European workers in the first three months of 2007 - down 16,000 on the last quarter of 2006.
Some 41% of workers went into administrative or other white collar jobs - up from 25% in 2004.
The government also says that workers from the eight nations are increasingly filling gaps in the public sector.
Poles continue to make up the vast majority of economic migrants, representing more than 70% of those seeking work.
Immigration minister Liam Byrne said: "While it remains too soon to evaluate the full impact of the accession of Bulgaria and Romania, the early indications are that our policy of restricting access to the UK's labour market is helping to ensure that only those who have something to offer the UK are allowed to work here.
"We will continue to monitor how restrictions are working but will also look at other indicators."
The government says its planned changes to the migration system, due to be in place from 2008, will help ministers to assess the appropriate levels of economic migration.
But Sir Andrew Green, chairman of pressure group Migrationwatch UK, said the figures on the two new countries did not tell the whole story.
"This is not a huge number - but there could be others [who have not been counted] because the system is flawed.
"The important thing is that the flow of migrants is unchanged. We still have the massive levels of immigration that we have been experiencing."
But Danny Sriskandarajah, migration expert with the Institute for Public Policy Research, said drop in workers from some Eastern European nations was important to notice.
"Most of these people come from Poland," he said. "Its economy is still struggling. But if you look at some of the other countries, the numbers of those arriving in the UK have fallen dramatically as these economies grow."