How many billion people would be better off if allowed to immigrate to GB?

...

You can't fit billions of people in the UK. ( I guess that's not what you meant, but that's what it sounds like)

But a libertarian utilitarian would have his work cut out for him to overcome the basic tenets of non initiation of force and weighing everyone's utility equally to justify limiting immigration.

Well, an absolute libertarian could of course not justify the state doing anything. And a utilitarian could come up with arguments against unrestricted immigration - for one thing, perhaps it would be better to maintain at least some border controls but increase foreign aid? I'm not suggesting this is a good idea, it just doesn't seem immediatly ridiculous.