Yeah, and in fact and as Eddie mentioned in his wraparounds, the entire movie was filmed on Universal's Hollywood set, and another aspect of this film which I found very impressive considering how well the look of the film never seems to belie this fact.
I also got to wondering which of SoCal's old horsetrack racing venues might have been used for those particular scenes where the races are shown being run in British clockwise fashion.
(...the old and now gone Hollywood Park or maybe Santa Anita, perhaps?...the IMDb webpage "filming location" page for this movie only specifies that the zoo scene was filmed at L.A.'s Griffith Park Zoo, but other than that just "Los Angeles")