Hi Seababa,
If your dad did not note the aircraft letter in his logbook it will by very difficult to find unless you come accross a photograph of that Hampden. Did you try the sqn’s Operations Record Book for the period in question (all available on line now fm The National Archive)? Mind you, no guarantee that this will mention the individual aircraft letters of their Hampdens. The RAFM in Hendon (Dept of Research and Information Services, aka DoRIS) probably hold the aircraft loss card but I don’t know if these cards also mention the aircraft letter. Worth the try though as the people at DoRIS are most helpful.
Alternatively I suggest you also post your request on the RAFCommands.com forum as some of the chaps or ladies there may be able to help you further.
Best of luck,
Walter