I think some of the statistics might be a bit off the mark according to
this article, with Germany well ahead at 197,540, France at 129,735 and Spain at 83,385. The
UK▸ numbers come next at 81,130 above all of the rest of
EU» countries. On that first link one can expand the graph to see them all.
So I don't think we are not pulling our weight here. Of interest, look at the asylum rejection rates. The House of Commons report states that the UK rejection rate was 24% in 2022. Compare that to France for example in my first link or even Spain and compare the numbers of accepted asylum seekers. I am not anti-asylum nor anti-immigration.
Of course, gathering statistics on those who 'disappear' into a country after arriving through illegitimate means is very difficult. But the UK's detection, detention and deportation rates don't show any significant differences to those of other European nations.
This is the nub of my comment on 'uncontrolled immigration' that it is the open and porous state of British society and its economy that people can simply disappear. I would love to study the statistics quoted above but I suspect that in the UK without its national identity card (needed for all walks of life in the EU and elsewhere), the 'detection' element, compared to EU areas, is significantly lower.