A pedantic point: the border between Scotland and England has never been Hadrian's Wall, just the kingdoms which preceded them.

Hadrian's Wall was a relatively brief frontier in the first place. The frontier of the Roman Empire in Britain fluctuated over its tenure, when Romans would drive north into the Clyde and Forth Valleys in central Scotland. For years, the Antonine Wall on the Forth-Clyde Isthmus was the frontier of Britannia.

For centuries after, the border fluctuated. Parts of Scotland and England were always at war, and so the border was always changing. For example, in the 10th century, the border was the Firth of Forth in the eastern Scottish lowlands (Northumbrian-Pictish border), bit in the 13th century, the Solway-Tweed line marked the border between England and Scotland, instituted by the Treaty of York in 1237.

The Scottish Marches is a term used to describe the land around the border during medieval and early modern times. People on each side of the border changed their allegiance between Scottish and English crowns several times to suit their family's interests. It was also largely lawless, as rogue clans known as the "Borders Reivers" terrorised and pillaged the land and its people in the name of revenge for years between the thirteen and seventeenth century.

However, the Border as it is now was largely a result of the Treaty of York, solidified by the Union of Crowns in 1603 (which allowed James VI of Scotland, the monarch who ended the lawlessness in the Borders which he named the Middle Shires, to take the British throne) and the Acts of Union in 1707.