>>and as far as I know it hasn't
>>non-EU immigration has increased hugely since Brexit.
Both things can be true at the same time.
If you run a British business it has become vastly more difficult to hire someone from the EU(where there is a lot of high skilled talent, especially in IT). Before Brexit if you found a candidate say in Spain, they could start working for you the next day, with the same paperwork as any British employee. Now if you wanted to hire the same candidate the hoops to go through to get them a visa are crazy and it takes minimum of 2-3 months to sort it out, not to mention the extra cost.
But since now the expense and effort for hiring EU candidates is roughly the same as hiring non-EU ones, is that really a surprise non-EU immigration has increased? Not to mention that EU candidates don't want to move to UK, and who could blame them - why accept a job on a 2 year visa that gives you and your family zero stability, when similarly paid jobs are available within the EU. And again - if you were going to bother with the whole visa nonsense why not go straight for US and get a much higher salary for the same job.
Just my 2c as an immigrant to UK.