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Student visa loopholes are allowing tens of thousands of people to enter the UK without any checks, shadow home secretary Yvette Cooper says.

Genuine foreign students were being blocked while short-term student visas were being increasingly abused.

In a speech in London, she admitted errors by the last government and said Labour must do more to recognise the economic impact of immigration.

Ministers say Labour let immigration get out of control while in power.

In her speech to the Institute for Public Policy Research, Ms Cooper admitted that Labour had not always got it right on the issue while in government and the impact of immigration must be properly managed so it was "fair for all".

She acknowledged that her party had not always been "ready to talk about problems" but said it knew that "that needs to change".

This will not mean a "move to the right", she argued, but would entail distinguishing between "immigration that works and immigration that doesn't".

"We will support the government where it introduces sensible policies and we will point out where they are getting things wrong," she said.

"But we won't enter an arms race of rhetoric on immigration - and we hope the prime minister won't either. That's not honest, or good for Britain."

She said fines for firms paying migrants less than the minimum wage should be doubled, councils should be given new enforcement powers to target rogue businesses and landlords and more opportunities created for British workers in sectors with high levels of foreign recruitment.

Ms Cooper told ´óÏó´«Ã½ Radio 4's Today that the reduction in net migration of 72,000 since the election has been caused by more Britons leaving the UK or choosing not to return, as well as a drop of 38,000 in students coming to study in the UK.

"Few think the answer to Britain's immigration challenges is to persuade more Brits to go away," she said.

She told Today the government's focus on meeting its pledge to reduce net migration by the tens of thousands meant it was failing to tackle problems in other areas - such as short-term student visas.

"Everything excluded from the net migration measure is being ignored - even if it causes serious problems," she said.

She claimed there were 150,000 reports about people possibly abusing student visas, which had not been checked by the UK Border Agency.

"Legitimate university students are included in the target even though they bring billions into Britain - and those are being squeezed. Yet student visitor visas aren't included - and growing abuse in that category is being ignored. Stronger checks are needed on shorter-term student visitor visas."

Ms Cooper said the number of such visas has gone up by 30,000 a year since the election even though applicants do not have to meet any academic requirements to be eligible and no checks are made on whether they study or overstay.

She also called for more to be done to stop illegal immigration, with the UK Border Agency carrying out unannounced inspections at colleges and workplaces and officials being given the power of arrest.

On the issue of migration from within the EU, she said it was right for the government to be looking at newcomers ability to access benefits and the health service but this must be done in a "sensible" way.

She said it must be made explicitly clear in the existing residency rules that migrants cannot claim Jobseekers Allowance within a few days or weeks of arriving and would be expected to live in the country for some time or to contribute before they get something back.

She also said a future Labour government would insist on maximum transitional controls on migration from countries joining the EU in future.

Immigration minister Mark Harper, responding to Ms Cooper's comments, told Today: "I don't think I heard an apology for Labour letting immigration get out of control while they were in power. We saw net migration of 2.2 million when they were in power.

"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.

He said Conservatives remained committed to reducing net immigration - the difference between people moving to and leaving the UK - to "tens of thousands" by the next election,