> "very biggest"? Doesn't "biggest" already cover very?

"very biggest" is a common phrase. Maybe it's more British.

> "near"? Wouldn't "nearly" be more grammatically correct.

I don't know but that's also pretty common.

> "but that was before commercial whaling"? Wouldn't a more professional way of writing this be "until the advent of commercial whaling"

I think it's fine.

> This all sounds like a speech of a tour guide being made towards children not a scientific article in the BBC.

The BBC is a government media / propaganda organization, "scientific BBC article" doesn't have much gravitas.