British Home Secretary John Reid said that Britain would take as many skilled workers as it needed, but said that those in low-skilled or unskilled jobs would have "no automatic right" to work in Britain.
Meanwhile Irish employment minister Micheal Martin said Bulgarians and Romanians will be required to seek work permits if they want to get jobs there after they join the bloc on January 1, 2007.
The British and Irish stances contrast starkly with their decision to adopt an "open door" policy when eight other former communist states were among 10 nations to join the bloc in May 2004.
British Prime Minister Tony Blair's administration had predicted that up to 13,000 people from eastern Europe would arrive in Britain after that enlargement. So far up to 600,000 have turned up.
However it wasn't all bad news for the open-access supporters.
Poland, the biggest newcomer in 2004, announced that it would open its jobs market to workers from all European Union member states as well as those from Iceland, Liechtenstein and Norway,
"We hope that our position will be an impetus to countries that are still hesitating," Deputy Labour Minister Kazimierz Kuberski said.
Nor is Poland alone in its embrace of all EU workers.
Fellow newcomers Slovakia, Estonia, and Latvia, plus the more-established Finland, have all promised to allow unfettered access to the new arrivals next year.
Sweden, along with Britain and Ireland, granted full access to new EU workers in 2004. Prime Minister Fredrik Reinfeldt has indicated that Sweden will probably not introduce any restrictions either for Romania and Bulgaria.
Many other member states have yet to announce a decision on the matter, with some adopting a wait-and-see approach as fellow EU members line up in the free-access or restrictions camps.
"It's not a decision that we want to take alone," said an Italian foreign ministry spokesman, "We are waiting to see what recommendations Brussels has on the question," he told AFP.
Other core EU states such as Belgium, France, Germany, the Netherlands and Spain are also in the "don't know" or at least the "haven't said" camps.
Germany, the biggest EU member, does not however appear to be dusting off the welcome mat.
In March, Berlin decided to extend to 2009 the restrictions on eastern European EU workers which had been due to expire last May.
A Commission spokeswoman made its position clear on Tuesday, noting that new countries had brought economic benefits to the 25-member bloc.
"We regret if member states who have opened for the 10 are not going to open for Romania and Bulgaria," said Katharina Von Schnurbein, the EU executive's spokeswoman for employment and social affairs.
"The economic implications have been very positive in the first two years after the last enlargement. We think that this is definitely a positive that should be taken into account," she said.
Workers from Romania and Bulgaria, which will become the EU's poorest members, crossed EU borders a long time ago in their search for a richer life.
They started heading westwards in their hundreds of thousands after the fall of the communist bloc in the late 1980s, entering illegally but hoping to later go legal.
Then immigration became easier in 2001 after the two aspirant EU members had visa requirements lifted for entering the bloc's border-free Schengen zone.
The Romanian presence is most felt in neighbouring Hungary, where 76 percent of all foreign workers are Romanians, 90,000 of whom have work permits.
Over 750,000 Bulgarians have emigrated since the fall of communism in 1989.

Copyright AFP (Agence France-Presse), 2006