Immigration and by that I mean settlement (not just conquest) into mainland Britain has been going on for centuries. You could make a case that from 1066 onward that conquest was not an issue, since the Normans settled in Britain, and in effect took over most of it. Although not all immigration was always legal, or indeed welcomed at the time, it did nevertheless have some natural self-controlling features and/or was of such a scale that allowed over time immigrants to establish themselves and prosper, and the population benefit from the skills and expertise of the newcomers.
The economic influences overall have been beneficial and really started in the last two centuries in a massive way with Irish immigration, this influx of people helped to build much of the roadways, canals and railways in mainland Britain from the late eighteenth/nineteenth century well into the early twentieth century. In the 1950's there were people from the West Indies, arriving to help plug the gaps left after WW2 losses, these are referred to now as the Windrush Generation. They were followed by many of East Asian descent, who had been driven out of Kenya and who brought business and commercial expertise with them.
Overall and over time there has been a constant stream of immigration as well emigration to and from Britain that has allowed the country to flourish, in particular when preparations can be made and some-managed control can be exercised, which aids ongoing assimilation.
Latterly, and it could be argued initially through the 'free movement' aspect of being in the EU people have arrived, in many cases unexpectedly, and in such numbers both from inside and outside Europe that the 'disturbance' this causes in many local communities, because it was poorly estimated and then badly mismanaged, that immigration has become a highly politicised issue, that defies basic common sense/logic. In part this is because the criminal element of the 'small boats' issue, regardless of whether asylum seeking people or those just wanting a better life, has been used to inflame passions and became one of the PM's promise to stop,;because the process is illegal.
Sunak recognises that this has some resonance with a great many people regardless of their politics and it is what the Tories are now counting on to 'batten-down the hatches' in their own party (and shut out Reform) and maybe able to pressure enough of the returning red wall voters to think twice in the GE. It won't overcome the genuine desire for change within the vast majority British public, or stop Labour gaining office, but it could take the shine of a Labour majority.
In any case the country will not take a proper and serious look at the implications for the future of having a planned and robust policy and resource commitment to immigration, until the small boat thing is sorted.