Edward I did win decisive victories against the Scots, at Dunbar and Falkirk, he stripped the Scottish King of his symbols of office and carried the Stone of Scone back to England - symbolically robbing Scotland of it's corronation throne - and before Robert the Bruce killed John Comyn in 1306 he had pretty much pacified the Scots for a year, but the reason why he couldn't perminantly tighten his grip on Scotland as he did was Wales was money.
His castle building projects in Wales, his town building work in Gascony, and his war with France meant he did not have the money to undertake a similar castle building project in Scotland, so he was unable to fully conquer Scotland through force of arms.
I've always felt that a united England and Scotland in this time period would have been more likely if Margaret, Maid of Norway had survived, reached adulthood and produced children of her own, because she would have been wed to Edward of Caernarfon, Prince of Wales and heir to the English Throne, thereby uniting the crowns and the countries through marriage, avoiding the bitter disputes of war and continuing the hitherto natural progression of ever-closer relations between England and Scotland that had been seen since the Norman Conquest.
Regardless of how Scotland might have been unified with England, Edward I himself was always going to distracted by European affair becuase his cousin.
Philip IV of France, wanted Edward's land in Gascony and conspired to rob him of them. He decieved his father-in-law (Edmund Crouchback, Edward's brother) into convincing the English King to relinquish his lands in a sign of submission as the Duke of Aquitaine for grace period after which his lands would be restored. Philip had no intention of honoring this arrangement and the second Edward fulfilled his part of it Philip declare the land forfeit because Edward had refused his summon, thereby starting a war between England and France, one which England was woefully unprepared for because it had been distracted with Wales and Scotland and preparing for a crusade, while France had used crusader funds to prepare itself for war with England.
Therefore, a Kingdom of Britain in the 1300's might be possible if Edward of Caernarfon and Margaret, Maid of Norway, saw out the reign of Edward Longshanks without upheavel in Scotland and united the crowns upon the death of the English King, but I consider it pretty impossible for Edward I himself to see such a union in his lifetime.