There is nothing inherently wrong with a rising population. In fact, if the UK were to have a fertility rate over 2.5 and had a rising population, that would be an immense success story. Even importing quality immigrants is not an issue in itself. We need the talented surgeons. We need the talented engineers. We need the talented entrepreneurs. What we don't need is freeloaders on top of the existing ones we have.
The issue here is the UK has welcomed hordes of illegal migrants that have all gone through safe countries such as France, Belgium etc and housed them in hotels, which are all being funded by the taxpayers.
Secondly, the UK has had an uncontrolled legal migration wave the last 5-10 years by welcoming people on cheap student and care visas but in reality have no inclination to work. Many of them have children which produces a strain on the education sector. Many of them have lots of health issues which puts a strain on healthcare and the waiting times. Many of them are being housed in social housing and if any of them are working, they'll be working in jobs that pay them via cash.
Even with all this said, I don't think it's a great thing to import hundreds of thousands of migrants from the third world and flood them in your major cities for social cohesion.
Except the actual number when it comes to population growth doesn't imply 'hordes'
You say 'many of them' a few times there but you have no actual figures to quantify if that is or isn't sustainable.
The cost could be helped by introducing a higher tax bracket for the ultra wealthy like Denmark and others have, and limiting pricks like Ratcliffe's tax evasion.
The countries they passed through don't have English as their first language and that plays a major part in their need, and why brexit didn't do anything but make others poorer.
Your final point, third world, is a designation put on them after the West pillaged their resources and rather than raising them up justified it through the theory of modernity and non interference. And by cohesion what do you mean? There are as many different attitudes and beliefs among those already living in the UK.
Everything you say just screams racism and xenophobia tbh no matter how you coat it, just like you were about trumps racism pre US election