The 1707 Act of Union formed Great Britain.
Its current form (from 1921) is the United Kingdom of Great Britain and Northern Ireland.
But it's more complicated than that. Wales was a colony of England from about 1282 until 1535 when it was annexed and became part of England proper. It was part of England proper until it was separated in 1955.
The crowns were united in 1603 when Elizabeth I died and James VI of Scotland became James I of England. The Union Jack was created to symbolize the united crowns in 1606.
For a short time under Oliver Cromwell England and Scotland were united under a single government, but they were then separated again until the Act of Union in 1707.
I used to love telling my English colleagues when they would play Germany and change "2 world wars and 1 world cup" that the royal family was more German than anything! The house of Saxe-Coburg-Gotha.
Also, I would love to tell them that for 200 years from William the Conqueror, their kings spoke only French and many, including Richard the Lionheart were born in France and died and were buried in France
And then that George I and II spoke only German etc. etc.
I was pretty popular ;-P (though in fairness to me, I do make fun of my own nationality and the English love the habit of "taking the p***" out of someone -- no thin skins like in some parts of the US