Completely out of control and unvetted immigration is not killing the UK because it is not happening. People applying to live and work in this country are subject to the widest range of checks possible based on available databases (though I understand our access to information has been reduced since Brexit).
The loosest controls on immigration in recent years was not introduced by the left but by the administrations of Johnson and Truss who believed that this would stimulate economic growth and led to a massive surge in arrivals. Although the mishandled it, they were recognising the hard truth that with our aging population and low birth rate, more young people have to come to this country if we still want triple lock pensions and a free at the point of delivery health service. Even Johnson and Triss didn't believe in uncontrolled immigration and checks remained in place. I've never met anyone, on the left or right, who doesn't believe in no controls or vetting. It is a fantasy that exists only in your head.
Obviously vetting is impossible for people arriving from failed states. These make up a very small proportion of arrivals. I'd be interested to see what your proposal would be on how to handle this problem. We are likely to soon see a renewed wave of people from Iran — if a young man presents himself in this country and says he wants asylum because he watched his sister being hung in a public square because she protested against the Islamic Republic — how will you check he doesn't have a criminal record — will you ask the IRCG?