Hello again Jayne
Well i have some across this in the War Office Records, which would include Royal Navy Personel.
Now although the actual Month of Birth shown is May and not June , there could well have been an Error made, or possibly that Wiliam just for some reason gave a wrong Month of Birth. But going by all other facts this indeed looks like it could well be William? (Mind you that June Month Shown on the Pic i posted with is details of Birth, is just the Quater in which People were Born)
The only way of course is to go ahead and apply for Copy, which when received will show the truth!
It may be worth the cost?
Hopefully it is him!
IN FACT I AM ALMOST POSITIVE !
Name: W H Lawlor . Service number: 14659203 . Date of birth: 13 May 1909 . | The National Archives
PS : If you do apply and get the Records would be great to see them on here. But thats of course up to you
Thanks