After the victory at Dunbar, King Edward overwhelmed the Scots completely, took many of their nobles into captivity, stripped their King of his titles and regalia before sending him off to exile, then he forced the Scottish nobles to pay homage to them as their leige and took all the symbols of Scottish monarch back with him to England.
What prevented him from affirming his control over Scotland was, actually, his conquest of Wales. He'd spent so much warring against the Welsh and building his castles there that he didn't have enough money left to build similarly impressive castles in Scotland and tighten his grip in the North. To say nothing of his attempts to raise funds for a Crusade, or the betrayal of his cousin, King Philip IV of France, that led to war between the two nation.
Money was in short supply, and money was what Edward needed to completely affirm his mastery of Scotland.