UK can stop anyone who is deemed national security from entering(if the worry is criminals coming here) and free movement applies only if you're employed, a student or can demonstrate that you have enough funds to live here without assistance - without it you can be denied entry. So that should solve the issue of "immigrants coming here for benefits". Really, UK has full power over its borders, it just chose not to exercise if.

You get it backwards, free movement of people is for workers, you don't have the right to stay if you aren't working (or alternatively studying, or living with someone who works) — though this isn't heavily enforced

You're right. I just looked it up to be sure. When I lived in the UK in 2007, Bulgaria and Romania entered the EU. There was some fuss about that, and initially those nationalities did not automatically obtain a work permit.

These were granted the same rights in 2014.

https://www.bbc.com/news/world-europe-25237742