* Immigration is major issue before 2015 election
* Labour planned strong criticism of Tesco and Next
* Dilutes criticism after firms deny allegations
* Climb-down is embarrassing for Labour
By Andrew Osborn and Peter Griffiths
LONDON, Aug 12 (Reuters) - Britain's Labour party toned down its criticism of retailers Tesco, and Next on Monday, a day after it said it planned to accuse them of favouring cheaper workers from Eastern Europe over British employees.
Chris Bryant, a senior lawmaker and the opposition party's spokesman on immigration, changed the wording of a speech he delivered on Monday morning to water down some criticism and retract some allegations altogether.
The climb-down is embarrassing for Labour which is trying to convince voters it is serious about controlling immigration ahead of a national election in 2015, conceding it made "mistakes" on immigration when in power from 1997 to 2010.
Labour is ahead of the ruling Conservatives by about seven percent in opinion polls, but some polls estimate its lead is much slimmer and its support has dropped in the last month.
Polls show immigration is one of the subjects that worries British voters the most and that many expect political parties to show they have a plan to tackle what they regard as excessive levels of immigration.
On Sunday, advance extracts of Bryant's speech showed he planned to accuse Tesco, Britain's biggest retailer, of making it difficult for British workers to relocate after closing down a distribution centre by telling them their pay would be cut.
"The result? A large percentage of the staff at the new centre are from (the) Eastern bloc," he planned to say.
But on Monday, he dropped the reference to pay being cut and avoided directly referring to Eastern Europe, saying simply that workers said they would have lost out in any move, showing how "sensitive" the issue of low-skilled migrant workers had become.
He also diluted planned criticism of Next, Britain's second-biggest clothing retailer, dropping an allegation that their use of Polish workers meant it was able to skirt British labour laws that would make hiring comparable local workers more expensive.
Both Tesco, which employs more than 310,000 people in 3,146 stores across Britain and Northern Ireland, and Next had said accusations contained in previews of the speech were untrue and contained factual errors.
"The statements in relation to Tesco are untrue," Tesco said on Twitter. "We work incredibly hard to recruit from the local area and we have just recruited 350 local people to work in our Dagenham site."
Retailer Next said it did hire Polish nationals to work in Britain at busy times, but said it did so because it could not find enough Britons to fill vacancies and that it was not doing anything unethical or illegal.
Bryant, whose speech spoke of "unscrupulous employers", said he never intended to suggest Tesco and Next were such, but stressed it was wrong that companies recruit so many overseas workers in areas of high unemployment.
"I am not backtracking from my basic point," Bryant told reporters after his speech in London. "How can it be that when you have 23.8 percent youth unemployment in an area that it is necessary to bring in 300-500 workers from elsewhere?"
Bryant also tried to calm the row by praising the two companies and saying he had hoped to inform a wider debate on immigration and employment.
The argument is awkward for Labour as it tries to tackle accusations voters are unclear what it stands for after it drifted from its Socialist roots when it was last in power from 1997-2010, and are unconvinced by leader Ed Miliband.
One senior Labour figure, health spokesman Andy Burnham, said in a newspaper interview at the weekend that the centre-left party must "shout louder and speak in a way that captures how people are feeling".
Labour suffered from a perception at the last election in 2010 that it had turned its back on working-class supporters and played down the impact immigration had had on their communities.
In one awkward incident, then Labour Prime Minister Gordon Brown was heard describing a supporter as a "bigoted woman" when she asked him about immigration on the campaign trail.
The issue is also a challenge for the Conservatives and Prime Minister David Cameron is trying to stop an exodus of voters to the anti-immigration UK Independence Party before the 2015 vote.
Cameron was criticised by his coalition partners, the Liberal Democrats, last month after the government sent vans on to the streets of London with billboards telling illegal immigrants to "go home or face arrest".