Consistently since records began British people have wanted less immigration.
Immigration laws only applied to the UK from the 1970s.
And even at that point it was never a majority that rejected immigration. There was a high anti German immigration movement before the first World War. But far from a majority of people cared.
And at every point where attitudes to immigration was increasing. Economic issues were also connected.
The majority of anti immigration event in UK history can very easily be linked to increases in the opinions being shared by newspapers owned and funded by wealthy production owners trying to silence working/poor people showing opposition to them.