Labour ditches opposition to a cap on the number of immigrants who can come to Britain Shadow home secretary Yvette Cooper admits Labour made mistakes in government She uses speech to IPPR think tank to say she now supports a cap on migrants but denies a 'lurch to the right' Shadow home secretary Yvette Cooper hinted that Labour could retain the coalition's cap on immigration Labour will concede today that it supports a migrant cap introduced by the Government. Just months ago, the Opposition claimed that the limit on highly skilled workers was the "worst of all worlds," doing little to control immigration and hurting scientific research and business. However, today Miss Cooper will admit the cap has not been harmful - and that a Labour government would support "sensible" Coalition policies. In a speech to the Institute for Public Policy Research think-tank, Miss Cooper will say: "We supported the Coalition decision to stop high-skilled workers coming to do low-skilled jobs. We will continue this policy. The Coalition introduced the limit on the small area of immigration policy it can actually control: the highly skilled migrant category. Workers from outside the EU can apply to come into the country through a points system, but the Government has limited migrants coming under the "tier-two" category to 20,700 a year. The highest earners, and those transferred by international companies to UK offices, are exempt. In the past year, just 9,421 applied to enter Britain under the tier-two visa. Miss Cooper will say: "We recognise the cap on "tier-two" workers has not caused the problems some businesses feared, though the implementation of it and the long delays in getting visas have caused difficulties." She will add: "If evidence shows it would not cause problems for our economy, we will maintain a cap." The coalition has applied a cap on the small part of immigration policy it can control- the highly skilled migrant category. In a party political broadcast last night, Labour leader Ed Miliband admitted that his part got immigration 'wrong in government' and promised more training for British workers to fill jobs Workers from outside the EU can apply to come into the country through the points system. The government has limited migrants coming under this "tier-two" category to 20,700 a year. The cap does not apply to staff who earn £40,000 or more and are transferred by their international companies to the their UK offices or to anyone earning more than £150,000 a year. A senior Labour frontbencher today blasts his own party for being too 'lazy' to win. Jim Murphy, the shadow defence secretary, told the New Statesman: "If you don't knock on people's doors between now and polling day you deserve what you get." His comments come after Labour was beaten into fourth place in last week's Eastleigh by-election, behind the Lib Dems, UKIP and the Tories. Mr Murphy added: "It's not an Eastleigh problem, it's a wider problem. It's Lazy Labour. There were parts of the party that had "a sense of entitlement to win." New Labour, Old Labour, left or right - you pay your money, you make your choice. There's honesty and sincerity about all of them. It's Lazy Labour we don't talk about. Mr Murphy also warned against counting on winning the election by watching the Liberal Democrat collapse. Winning 2010 Tory voters is much harder but much more important. We could scrape over the finishing line with Labour voters plus some ex-Liberals but given the scale of the problems we'd have to deal with, we don't want to just scrape over the finish line. We want a decent mandate. Mr Murphy warned that his party risked irrelevance in some parts of the country, adding: "I don't want it to become countercultural for people to vote Labour, the way it has become countercultural for people to vote Tory in Scotland....That's not a journey we can afford to take." Labour is also promising to tighten up access to student visitor visas, which are granted to those who intend to stay in the UK for under a year. UK Borders Agency staff should have the right to enter college premises and other businesses unannounced - and the power to arrest, she will say. Miss Cooper will also warn that while Labour will support the government on "sensible" policies, "we won't enter an arms race of rhetoric on immigration - and we hope the Prime Minister won't either. As Ed Miliband has said we know Labour got some things wrong on immigration in Government. We did tackle many of the serious problems in the asylum system we inherited after 1997. We also brought in stronger border checks,' she will say. But we should have been quicker to bring in the Australian style points based system. We should have kept transitional controls for Eastern Europe And we should have looked more at the impact, and been ready to talk about problems. So we know that needs to change. We will support the Government where it introduces sensible policies. And we will point out where they are getting things wrong. '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.' Her remarks follow leader Ed Miliband's "One Nation immigration" policy pitch made in a party political broadcast last night. It is the opposition party's latest attempt to show it is tuned in to voters" concerns after coming fourth in the Eastleigh by-election. It comes after figures showed net migration to Britain fell by a third in the year to June 2012. Home Secretary Theresa May is now drawing up radical reforms which would force immigrants to put up a cash bond to enter the UK.