It would appear the first version of God Save the Queen was released in 1619 by the English composer John Bull.

It was mid XVIII century, after the battle of Culloden in 1746, when this tune was sung in honour of George II and adopted as the British royal anthem. But other sources claim that God Save the King was written by the French Duchess of Brinon, with the title Grand Dieu sauve le Roi and the music composed by Jean Baptist Lulli, in 1686. There is a fact that corroborates this school of thought, being that with the Latin title Domine, salvum fac regem, this was the French royal anthem till the French Revolution. However, uncertainty persists...

Whatever the case, God Save the Queen, or God Save the King, in the case of a male monarch, is used as the national anthem by the British government, and recognised as the royal anthem by most Commonwealth countries.

The 1 minute instrumental version on this page is of very high quality. 

(c) PC FNCV

 God save our gracious Queen,
Long live our noble Queen,
God save the Queen !
Send her victorious,
Happy and glorious,
Long to reign over us,
God save the Queen !

O lord God arise,
Scatter our enemies,
And make them fall !
Confound their knavish tricks,
Confuse their politics,
On you our hopes we fix,
God save the Queen !

Not in this land alone,
But be God's mercies known,
From shore to shore !
Lord make the nations see,
That men should brothers be,
And form one family,
The wide world over

From every latent foe,
From the assassins blow,
God save the Queen !
Over her thine arm extend,
For Britain's sake defend,
Our mother, prince, and friend,
God save the Queen !

Thy choicest gifts in store,
On her be pleased to pour,
Long may she reign !
May she defend our laws,
And ever give us cause,
To sing with heart and voice,
God save the Queen !