shut until a valid and workable system
There are five legitimate reasons people can get a long term visa.
1. They're coming here to get a job, and have one lined up which meets a certain salary threshold, or they're coming to start a business and have investment funds.
2. They got married to a British person.
3. They have a British parent or grandparent.
4. They're a student, paying tens of thousands of pounds a year out of their own pocket.
5. They're joining a family member already in the UK.
Now, you might argue some students are bogus. Those at proper universities, not some dodgy "college", are genuinely here to enter higher education, and have to prove funding, obtain the grades or are postgraduates.
The fifth one, if the migrant is in a job where he can support them and pay their NHS surcharge, why shouldn't say, a doctor or researcher be able to bring their manager over with them? If they're on a 5 year NHS contract, they might not want to be separated from their family for that long. British nurses and medical staff are already heading to Australia where they can get paid better, and take their families with them.
Which ones of those reasons are unworkable, or uncontrolled?
1353 people across the whole of the UK is nothing. How many people left the UK in the same time period?