Was Great Britain united on the 24th March 1603 or 1st May 1707?

On the 24th March 1603 at between 2 a.m and 3 a.m, Queen Elizabeth 1 of England dies peacefully in her sleep. Her Heir and successor, her cousin King James VI of Scotland becomes King of England in addition to his being King of Scotland. But was this the date of British unity? The answer is yes, but not fully. I will begin with the role of Parliament in his day. The role of Parliament was to raise taxes and pass the laws and NOT to take over the reins of executive power unlike today. The role was very different. In the 22 years King James was King of England, the Westminster Parliament sat for 33 months in four Parliaments. The first parliament was from 19th March 1604, when King James gave his maiden speech, to 1610. The next one was just for two months in 1614 known as the addled Parliament as no new legislation was passed or new taxes raised. The third one was from 1619 to 1621 and was dismissed for interfering with foreign policy; the King's jurisdiction. The fourth and final Parliament was from 1624 to 1625 and was disbanded on the King's death as was the practice. As parliament was open for just 33 months over 22 years, the question of a modern day audience is this. Who ran the country? The simply answer is the King and Privy Councillors and not Parliament. There was clear division of the executive branch of Government, the King, and the Legislative branch; Parliament. King James was head of Government as well as head of state. His reign placed both Kingdoms under a single executive authority.