Greetings, and a warm welcome to Rootschat.
As your grandfather served in WW2 he would be approaching 100yrs old if still alive, so (although Rootschat has a policy of not naming living persons) it should be safe to let us know his full name.
Also, if you let us know your late grandmother's name, it could help track down a marriage and we can work with that. Your grandmother's maiden surname should be on a birth certificate of a child.
Also, if you can scan and post a photo of your grandfather in uniform (with the best view of any buttons or badges) we should be able to confirm if he was RAF or an army regiment.
Rootschatters can point you in the direction of free websites to search and many have specialist knowledge, so you have come to the right place!
All the best
Philip
(ADDED _ I am not sure if you would need proof of death to apply to the MOD as next of kin. If so, it would be useful if we can help find that out.)