Labour has called for a crackdown on some benefit payments to migrants as it backed the Government's immigration cap.
Shadow home secretary Yvette Cooper acknowledged public concerns about migrants from Romania and Bulgaria when restrictions are lifted in December.
In a major speech on immigration, she insisted action could still be taken to ease their impact although she did warn that Britain must not "pull up the drawbridge".
Ms Cooper suggested a "presence test" should be introduced to stop foreigners claiming benefits as soon as they arrive in the UK.
And she called for discussions with Europe about changing the rule that allows workers to claim family benefits even if their children still live in their home country.
Her address came as both Labour and the Tories continue to focus strongly on immigration after their poor performances in the Eastleigh by-election where UKIP surged to second.
Labour leader Ed Miliband admitted again on Wednesday that the party had mishandled immigration while it was in power.
And Ms Cooper continued the mea culpa, saying that it should have recognised it was such a major concern for the public and been "ready to talk about problems".
She promised Labour would now support "sensible policies" from the Government as she also sought to flesh out the Opposition's approach with specific measures.
The senior frontbencher insisted the party was not moving to the right and called for a distinction to be drawn between good and bad immigration.
Of the migrant cap, she said: "We recognise the cap on Tier 2 workers itself has not so far caused the problems some businesses feared ...
"If the evidence shows it would not cause problems for our economy, we will maintain the cap."
She condemned the Government's overall target to slash net migration by tens of thousands before 2015 as "too simplistic".
And she claimed there was a "growing catalogue of failure" in the coalition's attempts to tackle illegal immigration.
Ms Cooper called for tougher steps to prevent abuse of the system by people taking up short-term student visitor visas.
She claimed these had risen by 30,000-a-year since the last election, with no-one checking if they overstay or take up low-skilled jobs instead.
"Legitimate university students are included in the target even though they bring billions into Britain - and those are being squeezed," she said.
"Yet student visitor visas aren't included - and growing abuse in that category is being ignored. Stronger checks are needed."
She outlined a string of new measures, including:
:: doubling fines for employers who pay below the minimum wage and give councils the power to punish breaches;
:: stopping rogue landlords letting migrant workers live in over-crowded, over-priced accommodation;
:: proper exit checks with people counted in and out at the border;
:: maximum transitional controls for future countries joining the EU.
Ms Cooper said: "We need a sensible balanced approach. It is because immigration is important that it needs to be properly controlled."
Immigration minister Mark Harper said net migration hit 2.2 million when Labour was in power because the party had let the situation spiral out of control.
He insisted: "Our policy of reducing net migration has been successful so far. We've reduced net migration by a third.
"Most of that has been from a reduction of people coming into the country - 74,000 of the 84,000 reduction in net migration is a reduction in immigration. That's what the Office for National Statistics has said."
Ms Cooper's speech came as Home Secretary Theresa May was due to meet her German opposite number to discuss "welfare tourism" from Bulgaria and Romania when restrictions are lifted.
Hans-Peter Friedrich said ahead of the meeting that more EU regulation was needed to stop migrants settling in countries like Germany and the UK to claim benefits.