Johnboy, there is definitely a church there and I'm assuming that it is the same building that was there when your parents got married.
Most suburban Catholic parishes were created during the interwar years as the city expanded and quite often, in the early day's, masses and other services were held in temporary buildings until the parishes could afford to build a permanant church. This is why so many of Birmingham's Catholic churches are relatively modern, having been constructed during the forties, fifties and even as late as the early sixties.
As I remember it, SS Peter and Paul fits this description, although it's been a long time since I was there. However, it is possible that your parents may have been married in a temporary church building, which would of course have been replaced. If they were married in the permanant church, then I can assure you it is still there. If you get in touch with the Parish Priest, he should be able to tell you when the church was built.
Hope some of that makes sense.