Did the UK government in the film have any real choice other than to strongly restrict immigration?

Obviously it's morally wrong too treat the fugees the way they do. But if the UK is truly the only country left in the world that hasn't devolved into anarchy and everyone wants to escape there, how can that be remotely feasible? I feel like many of this film's fans (and possibly the filmmaker) believe they should just take all comers, but how is that at all practical? Once it becomes known that this is their policy, they will have literally billions of people trying to come to this island nation.

I'm sure people will read this and think I sound like Trump or something, but there's a big difference from our current geopolitical situation, with the United States being much larger than the UK, not to mention the world still having lots of other countries that people do want to live in. I just don't see how the UK alone could deal with the entire world flocking there without completely collapsing--and then they are just as bad off as everyone else. At which point they won't have immigrants flocking in, but the people who already live there will also be screwed. It's a kind of tragedy of the commons.