The biggest problem with the headline is that it assumes "immigrants" are a homogenous group. There could be some groups that are good for the country and some which are not, in which case you could still justify keeping the second group out. If you read the article it even says "However the report highlights that not all groups of migrants make a positive fiscal contribution to the UK and in some cases migrants can represent a burden for public finances."

Also, this doesn't count losses in utility that happen to locals because of immigrants but don't involve collecting benefits, such as increases in crime rates or unemployment rates.

That's quite interesting, and does refute a lot of the people who argue against all immigration. But the UK does have some forms of boarder control.