Buenchico has the answer so far as the Commonwealth goes.
Wales, not then I think a unified "country" was annexed to the English Crown by the conquests of Edward I and legally by the Statute of Wales 1284. This was followed by the Tudor Acts of 1536 - 1543 which brought the Welsh territories into complete unity with England.
England and Wales united with Scotland by the Act of Union 1707 to form Great Britain.
Ireland was added (all of it) by the Act of Union of 1800, and that lasted until 1922 when the Irish Free State came into being, leaving only Northern Ireland in the Union.