Given that, of the UKIP voters, only 7% voted Labour in 2010 (compared to 60% Tories and 15% Lib Dems), I think it's fair to say that this isn't true.
https://yougov.co.uk/news/2013/03/05/analysis-ukip-voters/
I'm just going to address this one by itself as its been bugging me most.
First, being anti-immigrant =/= voting UKIP. It's just not an accurate measurement. Labour voters with anti-immigrant sentiment could also just stay with Labour, go to the Tories, or stay home. Or they might have left the Labour party for the Tories a while back and are now moving on to UKIP. It's so patently not an accurate measurement that I don't know why you brought it up.
Second, the Labour party themselves have acknowledged this was an issue and tried to address it in their policies. There was even a mug for crying out loud! This?
This was real!
http://www.newstatesman.com/politics/2015/03/labours-anti-immigrant-mug-worst-part-it-isnt-gaffe
Do you think they produced that because Ed Miliband thought that would be a great joke for honouring his dad, or do you think they produced it because a significant proportion of Labour's core supporters are anti-immigrant?
It wasn't just last minute panic either -
http://www.theguardian.com/commenti...ukip-anti-immigrant-vote-ed-miliband-election - that's 2014, that's Diane Abbot not liking Ed Miliband "getting down in the gutter with Ukip to tussle for anti-immigrant votes." I have slightly mangled that quote in the sake of readability but it does reflect the tone of the piece.
This issue has been reported on in the media from every angle, from every wing of the press. Labour's acknowledged it, the research companies have reported it. Just a random grab bag of links on the subject -
http://www.theguardian.com/politics/2015/jul/18/labour-party-voters-desertion-election - 'It was also seen as anti-business, in the pocket of the unions and not tough enough on immigration. “Immigration is the topic that, left to their own devices, the respondents would have talked about all night. Their central arguments, across all groups and repeated frequently, were along the lines that our country is full, our country is broke and public services are creaking and cannot stand extra strain.â€'
http://www.newstatesman.com/politics/2015/05/say-it-again-labour-should-beware-ukip and
http://www.newstatesman.com/politic...labour-voters-drifting-ukip-or-not-voting-all - we clearly saw it being a problem in some core Labour seats up north.
And by core Labour seats, we mean those with large numbers of white working class - "It said that while Labour’s middle-class support held up, the party did badly amongst blue collar voters, many of whom went to the Tories or Ukip." -
http://www.theguardian.com/politics...tion-what-it-needs-next-smith-institute-study
It's not even like this is new! 2010, you've got this: "The regrets and half-apologies for Labour’s mass immigration policy are starting. The Eds, Balls and Miliband, and Jon Cruddas have all accepted that too many people came in too quickly. Ed Miliband told Andrew Marr on Sunday that the costs and benefits of mass immigration were very unevenly distributed and too many of the costs fell on Labour’s core working class voters. Jon Cruddas described the policy as acting like an unforgiving incomes policy for those in the lower part of the income spectrum." -
http://labour-uncut.co.uk/2010/05/18/labour-must-become-the-anti-immigration-party-david-goodhart/
"Rather, the party draws much of its support from working class voters (many of whom voted Labour in 2005 before defecting to the Tories in 2010) alienated by the collapse in living standards and the lack of good jobs." -
http://www.newstatesman.com/politics/2014/03/ukip-threat-labour-not-north
The Fabian Society said it was a problem -
http://www.fabians.org.uk/revolt-on-the-left-labours-ukip-problem-and-how-it-can-be-overcome/
The Economist noticed the problem -
http://www.economist.com/blogs/blighty/2014/06/labours-electorate
From Frank Field, in the Indie - Mr Field added: “In my lifetime, we’ve moved from a Labour Party which was working class-dominated. Some trendy London middle class went along with it but [were] subjected, at least publicly, to the moral economy of the working class.
“We’ve moved to a stage where what was that minority is in a governing position, which imposes upon the working class its moral economy… there is a real crisis of representation.†-
http://www.independent.co.uk/news/u...-need-own-citizenship-ceremonies-8559004.html
And the Telegraph back in 2009 -
http://www.telegraph.co.uk/comment/...s-betrayed-tribe-the-white-working-class.html
And I will stop here as either you've got the message or you refuse to listen to it at any costs. There are Labour voters - or in some cases ex-Labour voters - for whom anti-immigrant messages are music to their ears. There are core supporters who are crying out for Labour to hear them on this issue.
That is not to say they are the majority or that there aren't Labour core supporters who wouldn't be appalled by this. But that's not the point really. The point is to suggest that Labour don't have issues with immigration, as you did, that pro-Immigrant is the way to Labour supporter's hearts, just is not backed up.