No, England Scotland and Netherlands were never one country, but they were ruled by the same monarch.

James II of England and VII of Scotland was overthrown by a protestant revolution, who placed his daughter Mary and her husband William III of Orange on the thrown. William and Mary never had any children, so on their death England and Scotland reverted back to Mary's younger sister, Anne.

Hannover also joined with Britain in a similar way - Anne died without children and a law banning catholic's from inheriting meant the throne went to a distant cousin, George of Hannover. Hannover has laws against women inheriting, so when Victoria became queen of England, Hannover went to her uncle.

They were more like alliances than full unions. The countries would still have been run separately, but they would cooperate militarily. There would also be more open trade and immigration between the countries.

(personal anecdote - some of my ancestors came to the UK from the Netherlands during William & Mary's reign)