Since I posted this four years ago, there is now accessible information about the usage off words.
It appears that the word 'automobile' reached its peak in usage in USA and Britain at different times. The charts below compare 'car' with 'automobile', but the frequency of 'car' can be misleading, because it has many other aplications, beside the automobile. For example, the American 'railway car' is called a 'wagon' in Britain.
The charts below show that "automobile" reached its peak in America in the early 1930s, then went into great decline, replaced by 'car'. In Britain, "automobile" was always much less commonly used, and it peaked about a decade later, and is still used almost as much as it was then.
https://books.google.com/ngrams/grap...mobile%3B%2Cc0
https://books.google.com/ngrams/grap...mobile%3B%2Cc0