The Government should be preparing for the impact Bulgarian and Romanian migrants will have on schools and housing instead of alarming the public and announcing "symbolic gestures", a report said.
The UK will be able to absorb the expected influx of migrants next year if ministers adopt contingency measures to deal with pressures arising in local areas, t he centre-left think tank Institute for Public Policy Research said.
EU restrictions on movement of Bulgarians and Romanians will be lifted on January 1.
Plans to restrict migrants' rights to benefits are being rushed through Parliament, with immigrants from all EU states having to wait three months before being able to apply for jobseeker's allowance and other out-of-work benefits.
The report comes after Business Secretary Vince Cable yesterday insisted a cap in EU migrants is "not going to happen", accusing the Tories of panicking over immigration.
Deputy Prime Minister Nick Clegg has also pledged to block any fresh attempts to curb EU immigration, dismissing Home Office proposals for a 75,000 cap on migrants as "pointless".
The IPPR suggested that h elping local authorities deal with a possible increase in demand on school, housing stock and policing would be more helpful than last-minute "gestures" such as tightening benefit restrictions or increasing border presence.
Its report said there is no way to accurately estimate how many Romanian or Bulgarian workers might come to the UK next year, but said the situation now was different from 2004, when citizens from eight countries were granted free movement rights and full access to work in the UK.
The IPPR said that other EU countries lifting restrictions at the same time means the UK will not necessarily be the first choice for migrants, and that many Romanians and Bulgarians who wish to come may already be here, since citizens of both countries have been able to live and work here since 2007.
It also criticised the government for abolishing the Migration Impacts Fund, which helped local authorities with unexpected pressure on housing, schools and hospitals created by migration.
The fund, which was scrapped in 2010, helped authorities provide English language teaching for migrants, health awareness and extra means to deal with housing issues.
The challenges of increased demand for housing, public services, language needs and welfare entitlement needs to be prepared for, as well as planning to tackle potential exploitation of workers from the two countries and the integration of Roma migrants the IPPR said.
The institute recommends that a new fund should be set up to deal with short-term pressures over the first six months of 2014, and that a new Cabinet-level committee be established to specifically examine the impacts of EU migration.
IPPR senior research fellow Alex Gennie said: "It is entirely legitimate for politicians to be concerned about the pace and scale of European migration flows, not least because this is an issue about which there is so much public anxiety. But the political response has been more symbolic than substantive.
"Failure to properly prepare for the rapid inflow of citizens from the previous group of eight states in 2004 and the effects that this had on communities was short-sighted, and led to a number of avoidable problems. It also polarised the broader migration debate in the UK."
She said the UK has had 10 years of experience in managing the impact of migration from these countries, adding: "The past decade has shown that the UK's economy and society are flexible enough to adapt to and benefit from European migration flows, as long as the pressure points they create are quickly identified and addressed.
"There is little to suggest that these lessons have been learned and applied in the run up to January 1, but even now it is not too late to take some practical steps to alleviate any issues that might arise."