Just because people seem confused on all this (for some reason).
Before 1535, England, Wales, Ireland and Scotland were legally separate countries. Following the English conquest of Ireland in the 12th century and of Wales in the 13th, England, Ireland and Wales had a single ruler, who was styled King of England and Lord of Ireland, but were administered as separate countries. Scotland had a completely separate king.
However, Henry VIII is often seen as a chap who shook things up a bit, and relations between the Home Nations were no exception.
Between 1535 and 1543, the Laws in Wales Acts extended English law to Wales, replaced Welsh local government with an English model, and gave Welsh constituencies representation in the English parliament. After 1543, Wales was effectively part of England from a legal/administrative point of view.
In 1542, the Irish Parliament’s Crown of Ireland Act made the King of England, whoever he might be, the king of Ireland; but unlike Wales, Ireland remained administered separately.
In 1603, King James VI of Scotland also became King of England (and hence, Ireland), as Elizabeth I’s nearest heir. Although James liked the idea of unifying his territories, both the English and Scottish aristocracy and parliaments told him roundly to piss off. So at this point, James was king of the independent states of England (including Wales), Ireland and Scotland, in much the same constitutional way that Elizabeth II is queen of the independent states of the United Kingdom, Canada and Australia. Although obviously, he had rather more power then than she does now…
By 1706, following failed attempts throughout the 17th century, the Scottish aristocracy eventually accepted the concept of union between the two countries (largely because Scotland was bankrupt following its disastrous colonial adventures in central America). In 1707, each country’s parliament passed an Act of Union, creating a united kingdom of England and Scotland – referred to as Great Britain – with a single parliament, a free trade area and a single currency, although Scotland retained its unique and separate legal system, and the established Church of Scotland was not integrated into the Church of England or fully controlled by the UK monarch or parliament [see Chris in comments]. All laws of either nation that were incompatible with the Act were repealed by the Act. At this point, Queen Anne became Queen of Great Britain and Queen of Ireland.
In 1800, the parliaments of Great Britain and Ireland each passed another Act of Union, creating a united kingdom of Great Britain and Ireland, referred to imaginatively as the United Kingdom of Great Britain and Ireland, with a single parliament, a customs union, and a single currency – a similar drill to 1707. Part of the deal to gain Irish acceptance was that Catholics would be given the right to vote in and stand for the UK parliament (previously, only Protestants were eligible to stand for either parliament) – although this was later vetoed by King George III, much to the ire of the (posh, Catholic segment of the) Irish.
Unlike the 1707 Act, which was legitimately voted for by the Scottish parliament, the passage of the 1800 Act in the Irish parliament was driven by epic bribery, as well as by the lies about Catholic emancipation. The Catholic Relief Act was eventually passed in 1829 – too late to stop the Irish from being deeply and fairly pissed off about the whole event.
A few years after (most of – see Thumb in comments and my reply) Ireland effectively seceded from the Union in 1921 to form the Irish Free State and hence lost its representation in Westminster, the legal name of the remaining entity was changed to the United Kingdom of Great Britain and Northern Ireland in 1927. King George V became King of the United Kingdom (including Northern Ireland) and King of (most of) Ireland.
(Most of) Ireland declared itself a republic in 1948, at which point King George VI ceased to be King of (most of) Ireland – although bizarrely, the Republic of Ireland parliament didn’t repeal the Act of Union until 1962.
The recent devolution in Scotland, Wales and Northern Ireland, although massively important in practice, hasn’t changed the overall legal status of of the above – we’re still in the same position as in 1948. The state of which Elizabeth II is queen is still the United Kingdom of Great Britain and Northern Ireland, and the UK Parliament is still sovereign over the four nations that make up the state.
Sources: Laws in Wales Acts (1535, 1543), Crown of Ireland Act, 1707 Acts (England, Scotland), 1800 Acts (Great Britain, Ireland), Anglo-Irish Treaty 1921, Royal & Parliamentary Titles Act 1927, Republic of Ireland Act 1948, Statute Law Revision (Pre-Union Irish Statutes) Act 1962.