Hadrian’s Wall in Britain wasn’t really to keep out the barbarians from north of the wall. The previous emperor Trajan had fought some wars that showed that the empire had overreached what it could hold so Hadrian decided to pull back to more manageable borders that weren’t so expensive to keep with massive standing armies. In Britain this wall was more of an effort to control the movement across the area and possibly to tax goods across the land.

(Book – Hadrian and the Triumph of Rome – Anthony Everitt)