I'm actually going to give this a proper response.
We don't have unfettered immigration, which is the current right wing belief. Its false though.
An overview of net migration in the UK – defined as the difference between immigration and emigration of people moving for at least a year.
migrationobservatory.ox.ac.uk
Only 14% of people in this country were born outside of the UK. This is generally in-line with our neighbours and below many of our allies including Canada, New Zealand, Australia, Belgium, Sweden, and Ireland where as much as 20% of the population can be born outside of their nations.
Asylum Migration is incredibly low, the majority are students (who are largely temporary) and those who are here on work visas. Breaking it down, the article shows Non-EU Migration but its representative.
Highest is work visas at 423,000 - these will require a sponsorship - so have obtained a sponsored employment position with a business or organisation that follows UK employment visa regulations such as filling in-demand industries, generally require a high level degree unless in specific critical demand industries such as healthcare. The critical demand list is flexible and changes regularly, outside of that you need to be highly qualified and have a sponsored job offer which is selective and hard. They also need the means to sustain themselves.
Next are students at 379,000, who for some weird ass reason became a target for immigration criticism. You want us to have a world class education system but they whinge about students. They are here to study, have to have an offer and sponsorship from a UK University, and have to have their annual course fees and living costs in the bank as part of their visa application. Thats between £30,000 and £60,000 per year depending upon the university. There is the work transition option but thats selective and the vast majority leave after study, only 8% stay on a grad visa and 11% on skilled worker routes (i.e. high demand/healthcare). This number fluctuates wildly year on year too.
Your 700k per year, well near 400k are students who are here for between 1-3 years. Its dense as hell.
Everything else, so asylum, marriage/couples/family, and other are between 20,000 and 80,000. Marriage and Couples Visas have high income attachments so are more for wealthy people, bringing family is not automatic so family visas are also restrictive.
So what are people moaning at? That we have a lot of work visas? Then educate more people and promote those industries. Its expensive to sponsor visas, most companies don't. Too many students? Idiotic. Asylum? Small minority. Couples? thats already discriminatory and a small minority. Family, also highly restrictive and a tiny minority.
You just answered your own question.