"The United Kingdom of Great Britain as stated in artical 4 of the Acts of Union. Ireland joined the UK in 1801 but left about 120 years later, so you are playing with words but cannot alter the substance."

To be fair though there is a subtle difference in the wordings Jim. In the 1707 Treaty of Union as passed through the Scottish parliament it definitely states that a new United Kingdom is being created and article after article repeats that phrase United Kingdom. However article one deals with the name and specifically states "be united into one Kingdom by the name of Great Britain". It reads to me afterwards that the term United Kingdom is being used to describe Great Britain rather than being part of the official name. However in the 1801 Act with Ireland it specifically states that the name of the new kingdom "shall be the United Kingdom of Great Britain and Ireland"