Depends what you failed on.
The Royal Navy require good pilot and observer (navigator/WSO-type) scores in the aptitude test to consider you for pilot.
If you failed to get into the RAF on a more subjective trait like leadership potential, then give the RN a go. It's not that their standards are lower, but they will look at you from a slightly different angle and you may do better on the day.
In other words, DO NOT GIVE UP on the basis of 1 knock-back.