The Armed Forces of the United Kingdom, Canada, Australia and New Zealand all swear allegiance to Queen Elizabeth II. The only Service that does not swear allegiance is Britain's Royal Navy, because it was formed by a Monarch, Queen Elizabeth I, and not by Parliament, and its allegiance is therefore implicit in its very existence.
The Royal Air Force Oath of Allegiance is sworn on the very first day of training, both by recruits and officer cadets. It is broadly similar to most other Oaths of Allegiance, and runs thus (I'll use my name):
"I, Andrew James Wasley, Swear by Almighty God that I will be Faithful and bear True Allegiance to Her Majesty Queen Elizabeth II, her Heirs and Successors, and that I will, as in Duty bound, Honestly and Faithfully Defend Her Majesty, her Heirs and Successors, in Person, Crown and Dignity against all Enemies and will Observe and Obey all Orders of Her Majesty, her Heirs and Successors, and of the Air Officers and other Officers set over me."