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the days when low pay and cheap labour are part of the British way on growth must end.
That bit, right after the word but.
I think it's possible to be welcoming and open to immigrants of all kinds whilst still wanting to improve things for those already in the country so that there isn't a reliance on cheap, exploitative labour. Whether Keir is getting that across well I'm not so sure, the headlines certainly aren't, but maybe they're aimed at people who only read the headlines and care not for immigrants.
Maybe it's in the source but I didn't see any of those points in the bit quoted.
I get the desire to give him the benefit of the doubt, but if you take him on his words it's skirting near some pretty ugly stuff. It's a mark of how Brexit has moved the Overton window in UK politics.