It might depend on who you talk to at the history centre but I don't see why you just cannot ask for information on who lived at the address you are interested in from around the date of the marriage till after the birth of the last child (no information is held I think between 1940-44).
If they are unable to help (even for a charge) you could try to find someone who can go there to look at the register for you (I've had success like that before but haven't needed to look in Wiltshire)