Like many other European social democratic parties, Labour is moving right on immigration, certainly driven by the recent success of Reform. We have researched this question for years now. There is an abundance of evidence of why this isn't a good strategy. A thread summarizing some of our research
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A strong motivation for “getting tough on immigration” is the narrative that social democrats have lost the working class to the radical right. Empirically this is false. Only few former SD supporters now vote for the radical right.
https://politicscentre.nuffield.ox.ac.uk/media/1awhrcvv/abouchadi_etal-090124.pdf
Our research shows that when established parties move to the right on immigration this does not weaken the radical right but if anything strengthens them. It contributes to their normalization and legitimation
https://doi.org/10.1017/psrm.2022.8
More socially conservative positions do not help SD parties electorally. They are not correlated with more working class support. However, they are associated with less support among educated and young voters. https://doi.org/10.5167/uzh-187786