The call was just for show? A possibility.
If you're going to have a cover story you have to make it look good.
I considered that possibility, but it doesn't fit the way the scene is staged. There's no need for a cover story if Holmes is going to go and sit on a park bench down a quiet street far from home away from Watson's prying eyes to place his call.
I also considered that "my father" was a code word that Holmes uses to access his resources. I can't dismiss this one as easily.